1 00:00:30,000 --> 00:00:50,000 Can you see the board? 2 00:00:50,000 --> 00:00:56,000 Yes, I can see it. 3 00:00:56,000 --> 00:01:06,000 Ok, let's start now. We continue with first-degree equations with parentheses. 4 00:01:06,000 --> 00:01:16,000 First-degree equations 5 00:01:16,000 --> 00:01:28,000 with parentheses. 6 00:01:28,000 --> 00:01:32,000 I'm going to make a few examples here and I'll put two for you to see. 7 00:01:32,000 --> 00:01:46,000 Let's try. The first one is easy. It would be 3 times x plus 1 equals x. 8 00:01:46,000 --> 00:01:50,000 So, the first step, what would it be? 9 00:01:50,000 --> 00:01:58,000 Remove parentheses. 10 00:01:58,000 --> 00:02:08,000 That is, 3x plus 3 equals x. 11 00:02:08,000 --> 00:02:12,000 I multiply the monomial by the polynomial. 12 00:02:12,000 --> 00:02:16,000 3 times x, 3x, and 3 times 1 equals x. 13 00:02:16,000 --> 00:02:20,000 The second step, what would it be? It's the same as before. Transpose. 14 00:02:20,000 --> 00:02:30,000 Transpose. That is, 3x minus x equals 3. 15 00:02:30,000 --> 00:02:38,000 The third step is to simplify. 16 00:02:38,000 --> 00:02:42,000 2x equals 3. 17 00:02:42,000 --> 00:02:48,000 And the fourth step is to simplify. 18 00:02:48,000 --> 00:02:56,000 x equals 3 divided by 2. 19 00:02:56,000 --> 00:02:58,000 And that's it. 20 00:02:58,000 --> 00:03:08,000 We have one more step, which is to remove parentheses. 21 00:03:08,000 --> 00:03:12,000 I'm going to make another example. 22 00:03:12,000 --> 00:03:40,000 Here, 2 times x plus 1 equals 3 times x minus 2. 23 00:03:40,000 --> 00:03:48,000 Another example. 24 00:03:48,000 --> 00:03:50,000 Well, let's see. 25 00:03:50,000 --> 00:03:54,000 First we said, remove parentheses. 26 00:03:54,000 --> 00:04:00,000 First, remove parentheses. 27 00:04:00,000 --> 00:04:04,000 Remove parentheses. 28 00:04:04,000 --> 00:04:14,000 That is, 2 times x, 2x, plus 2 equals 3 times x minus 6. 29 00:04:14,000 --> 00:04:18,000 We multiply 2 times x, 2x, and 2 times 1 equals 2. 30 00:04:18,000 --> 00:04:22,000 3 times x is 3x, and 3 times minus 2 is minus 6. 31 00:04:22,000 --> 00:04:28,000 The second step, what would it be? Transpose. 32 00:04:28,000 --> 00:04:30,000 Transpose. 33 00:04:30,000 --> 00:04:36,000 So it would be 2x minus 3x. 34 00:04:36,000 --> 00:04:38,000 This passes subtracting. 35 00:04:38,000 --> 00:04:42,000 And the 2 that is adding, passes subtracting. 36 00:04:42,000 --> 00:04:44,000 Minus 6, minus 2. 37 00:04:44,000 --> 00:04:52,000 The third step would be to simplify. 38 00:04:52,000 --> 00:04:54,000 Simplify. 39 00:04:54,000 --> 00:04:58,000 Minus x equals minus 8. 40 00:04:58,000 --> 00:05:02,000 And the fourth step, clear. 41 00:05:02,000 --> 00:05:10,000 x equals minus 8 divided by minus 1 equals 8. 42 00:05:10,000 --> 00:05:12,000 x equals 8. 43 00:05:22,000 --> 00:05:28,000 If we substitute here x times 8, we get 8 and 8. 44 00:05:28,000 --> 00:05:30,000 9 times 2 equals 18. 45 00:05:30,000 --> 00:05:32,000 Here we get 18. 46 00:05:32,000 --> 00:05:34,000 And here 6 times 3 equals 18. 47 00:05:34,000 --> 00:05:36,000 Also. 48 00:05:36,000 --> 00:05:38,000 The proof. 49 00:05:46,000 --> 00:05:48,000 Let's do another case. 50 00:05:52,000 --> 00:06:14,000 For example, 3 times x minus 2, minus 2 times x plus 3 equals 0. 51 00:06:14,000 --> 00:06:16,000 Let's do another example. 52 00:06:16,000 --> 00:06:18,000 Well, the first step. 53 00:06:18,000 --> 00:06:22,000 Remove parenthesis. 54 00:06:22,000 --> 00:06:34,000 That is, 3 times x equals 3x. 55 00:06:34,000 --> 00:06:36,000 3 times minus 2 equals minus 6. 56 00:06:36,000 --> 00:06:40,000 Minus 2 times x equals minus 2x. 57 00:06:40,000 --> 00:06:44,000 And minus 2 times 3 equals minus 6. 58 00:06:44,000 --> 00:06:48,000 The second step. 59 00:06:48,000 --> 00:06:50,000 Transpose. 60 00:06:50,000 --> 00:06:52,000 Transpose. 61 00:06:52,000 --> 00:06:56,000 3x minus 2x equals. 62 00:06:56,000 --> 00:06:58,000 This would be equal to 0. 63 00:06:58,000 --> 00:07:00,000 Equal to 0. 64 00:07:00,000 --> 00:07:04,000 It would be equal to 6 plus 6. 65 00:07:04,000 --> 00:07:06,000 This passes adding. 66 00:07:06,000 --> 00:07:08,000 Passes adding. 67 00:07:08,000 --> 00:07:12,000 The third step is to clear. 68 00:07:12,000 --> 00:07:14,000 Simplify. 69 00:07:14,000 --> 00:07:16,000 Simplify. 70 00:07:18,000 --> 00:07:22,000 That would be x equals 12. 71 00:07:22,000 --> 00:07:24,000 And it would be directly solved. 72 00:07:24,000 --> 00:07:26,000 No need to complain. 73 00:07:26,000 --> 00:07:28,000 x equals 12. 74 00:07:36,000 --> 00:07:40,000 One more step than the previous equations we saw. 75 00:07:40,000 --> 00:07:42,000 Remove parenthesis. 76 00:07:46,000 --> 00:07:48,000 Let's see one last example. 77 00:08:00,000 --> 00:08:02,000 4 times x minus 3. 78 00:08:04,000 --> 00:08:06,000 Minus 7 times x minus 4. 79 00:08:10,000 --> 00:08:12,000 Equal to 6 minus x. 80 00:08:14,000 --> 00:08:16,000 The first step. 81 00:08:18,000 --> 00:08:20,000 Remove parenthesis. 82 00:08:30,000 --> 00:08:32,000 4 times x minus 12. 83 00:08:34,000 --> 00:08:36,000 Minus 7 times x minus 28. 84 00:08:40,000 --> 00:08:42,000 Equal to 6 minus x. 85 00:08:56,000 --> 00:08:58,000 The second step. 86 00:09:00,000 --> 00:09:02,000 Transpose. 87 00:09:06,000 --> 00:09:08,000 4 times x minus 7 times x. 88 00:09:10,000 --> 00:09:12,000 Plus x. 89 00:09:16,000 --> 00:09:18,000 This minus x passes adding. 90 00:09:18,000 --> 00:09:20,000 With plus sign. 91 00:09:20,000 --> 00:09:22,000 And here we would have equal to 6. 92 00:09:26,000 --> 00:09:28,000 Plus 12. 93 00:09:30,000 --> 00:09:32,000 This passes adding. 94 00:09:32,000 --> 00:09:34,000 And the 28 passes subtracting. 95 00:09:34,000 --> 00:09:36,000 Minus 28. 96 00:09:36,000 --> 00:09:38,000 The third step. 97 00:09:42,000 --> 00:09:44,000 Simplify. 98 00:09:48,000 --> 00:09:50,000 Minus 2 times x. 99 00:09:50,000 --> 00:09:52,000 Equal to 6 minus 12. 100 00:09:52,000 --> 00:09:54,000 Equal to 18. 101 00:09:54,000 --> 00:09:56,000 Minus 10. 102 00:09:56,000 --> 00:09:58,000 And the fourth step. 103 00:09:58,000 --> 00:10:00,000 Clear. 104 00:10:02,000 --> 00:10:04,000 x equals. 105 00:10:04,000 --> 00:10:06,000 A minus 10. 106 00:10:06,000 --> 00:10:08,000 Divided by minus 2. 107 00:10:08,000 --> 00:10:10,000 Equal to 5. 108 00:10:18,000 --> 00:10:20,000 Remove parenthesis. 109 00:10:20,000 --> 00:10:22,000 Transpose. Simplify. Clear. 110 00:10:30,000 --> 00:10:32,000 I'm going to put one here. 111 00:10:32,000 --> 00:10:34,000 A couple of them. 112 00:10:36,000 --> 00:10:38,000 Let's see how. 113 00:10:48,000 --> 00:10:50,000 Come on, let's go with the first. 114 00:10:54,000 --> 00:10:56,000 10 times x plus 6. 115 00:10:58,000 --> 00:11:00,000 Equal to 50. 116 00:11:02,000 --> 00:11:04,000 Times x plus 2. 117 00:11:04,000 --> 00:11:06,000 Let's do this. 118 00:11:32,000 --> 00:11:34,000 Simplify. 119 00:11:34,000 --> 00:11:36,000 Clear. 120 00:12:02,000 --> 00:12:04,000 Misplaced. 121 00:12:04,000 --> 00:12:06,000 We'll be back there in a minute. 122 00:12:16,000 --> 00:12:18,000 5. 123 00:12:18,000 --> 00:12:20,000 6. 124 00:12:20,000 --> 00:12:22,000 2. 125 00:12:22,000 --> 00:12:24,000 3. 126 00:12:24,000 --> 00:12:26,000 4. 127 00:12:26,000 --> 00:12:28,000 5. 128 00:12:28,000 --> 00:12:30,000 4. 129 00:12:30,000 --> 00:12:31,980 9. 130 00:12:31,980 --> 00:12:33,980 10. 131 00:12:33,980 --> 00:12:35,980 11. 132 00:12:35,980 --> 00:12:37,980 12. 133 00:12:37,980 --> 00:12:39,980 13. 134 00:12:39,980 --> 00:12:41,980 14. 135 00:12:41,980 --> 00:12:43,980 15. 136 00:12:43,980 --> 00:12:45,980 16. 137 00:12:45,980 --> 00:12:47,980 17. 138 00:12:47,980 --> 00:12:49,980 18. 139 00:12:49,980 --> 00:12:51,980 19. 140 00:12:51,980 --> 00:12:53,980 20. 141 00:12:53,980 --> 00:12:55,980 21. 142 00:12:55,980 --> 00:12:57,980 22. 143 00:12:57,980 --> 00:12:59,980 23. 144 00:12:59,980 --> 00:13:01,980 24. 145 00:13:01,980 --> 00:13:03,980 25. 146 00:13:03,980 --> 00:13:05,980 26. 147 00:13:05,980 --> 00:13:07,980 27. 148 00:13:07,980 --> 00:13:09,980 28. 149 00:13:09,980 --> 00:13:11,980 29. 150 00:13:11,980 --> 00:13:13,980 30. 151 00:13:13,980 --> 00:13:15,980 31. 152 00:13:15,980 --> 00:13:17,980 32. 153 00:13:17,980 --> 00:13:19,980 33. 154 00:13:19,980 --> 00:13:21,980 34. 155 00:13:21,980 --> 00:13:23,980 35. 156 00:13:23,980 --> 00:13:25,980 36. 157 00:13:25,980 --> 00:13:27,980 37. 158 00:13:27,980 --> 00:13:29,980 38. 159 00:13:29,980 --> 00:13:31,980 39. 160 00:13:31,980 --> 00:13:33,980 40. 161 00:13:33,980 --> 00:13:35,980 41. 162 00:13:35,980 --> 00:13:37,980 42. 163 00:13:37,980 --> 00:13:39,980 43. 164 00:13:39,980 --> 00:13:41,980 44. 165 00:13:41,980 --> 00:13:43,980 45. 166 00:13:43,980 --> 00:13:45,980 46. 167 00:13:45,980 --> 00:13:47,980 47. 168 00:13:47,980 --> 00:13:49,980 48. 169 00:13:49,980 --> 00:13:51,980 49. 170 00:13:51,980 --> 00:13:53,980 50. 171 00:13:53,980 --> 00:13:55,980 51. 172 00:13:55,980 --> 00:13:57,980 52. 173 00:13:57,980 --> 00:13:59,980 53. 174 00:13:59,980 --> 00:14:01,980 54. 175 00:14:01,980 --> 00:14:03,980 55. 176 00:14:03,980 --> 00:14:05,980 56. 177 00:14:05,980 --> 00:14:07,980 57. 178 00:14:07,980 --> 00:14:09,980 58. 179 00:14:09,980 --> 00:14:11,980 59. 180 00:14:11,980 --> 00:14:13,980 60. 181 00:14:13,980 --> 00:14:15,980 61. 182 00:14:15,980 --> 00:14:17,980 62. 183 00:14:17,980 --> 00:14:19,980 63. 184 00:14:19,980 --> 00:14:21,980 64. 185 00:14:21,980 --> 00:14:23,980 65. 186 00:14:23,980 --> 00:14:25,980 66. 187 00:14:25,980 --> 00:14:27,980 67. 188 00:14:27,980 --> 00:14:29,980 68. 189 00:14:29,980 --> 00:14:31,980 69. 190 00:14:31,980 --> 00:14:33,980 70. 191 00:14:33,980 --> 00:14:35,980 71. 192 00:14:35,980 --> 00:14:37,980 72. 193 00:14:37,980 --> 00:14:39,980 73. 194 00:14:39,980 --> 00:14:41,980 74. 195 00:14:41,980 --> 00:14:43,980 75. 196 00:14:43,980 --> 00:14:45,980 76. 197 00:14:45,980 --> 00:14:47,980 77. 198 00:14:47,980 --> 00:14:49,980 78. 199 00:14:49,980 --> 00:14:51,980 79. 200 00:14:51,980 --> 00:14:53,980 80. 201 00:14:53,980 --> 00:14:55,980 81. 202 00:14:55,980 --> 00:14:57,980 82. 203 00:14:57,980 --> 00:14:59,980 83. 204 00:14:59,980 --> 00:15:01,980 84. 205 00:15:01,980 --> 00:15:03,980 85. 206 00:15:03,980 --> 00:15:05,980 86. 207 00:15:05,980 --> 00:15:07,980 87. 208 00:15:07,980 --> 00:15:09,980 88. 209 00:15:09,980 --> 00:15:11,980 89. 210 00:15:11,980 --> 00:15:13,980 90. 211 00:15:13,980 --> 00:15:15,980 91. 212 00:15:15,980 --> 00:15:17,980 92. 213 00:15:17,980 --> 00:15:19,980 93. 214 00:15:19,980 --> 00:15:21,980 94. 215 00:15:21,980 --> 00:15:23,980 95. 216 00:15:23,980 --> 00:15:25,980 96. 217 00:15:25,980 --> 00:15:27,980 97. 218 00:15:27,980 --> 00:15:29,980 98. 219 00:15:29,980 --> 00:15:31,980 99. 220 00:15:31,980 --> 00:15:33,980 100. 221 00:15:33,980 --> 00:15:35,980 100. 222 00:15:35,980 --> 00:15:37,980 100. 223 00:15:37,980 --> 00:15:39,980 100. 224 00:15:39,980 --> 00:15:41,980 100. 225 00:15:41,980 --> 00:15:43,980 100. 226 00:15:43,980 --> 00:15:45,980 100. 227 00:15:45,980 --> 00:15:47,980 100. 228 00:15:47,980 --> 00:15:49,980 100. 229 00:15:49,980 --> 00:15:51,980 100. 230 00:15:51,980 --> 00:15:53,980 100. 231 00:15:53,980 --> 00:15:55,980 100. 232 00:15:55,980 --> 00:15:57,980 100. 233 00:16:07,980 --> 00:16:09,980 100. 234 00:16:09,980 --> 00:16:11,980 100. 235 00:16:11,980 --> 00:16:13,980 100. 236 00:16:13,980 --> 00:16:15,980 100. 237 00:16:16,980 --> 00:16:18,980 1. 238 00:16:18,980 --> 00:16:20,980 1. 239 00:16:20,980 --> 00:16:22,260 1. 240 00:16:22,260 --> 00:16:24,260 One. 241 00:16:24,260 --> 00:16:26,260 One. 242 00:16:26,260 --> 00:16:28,280 Two. 243 00:16:28,280 --> 00:16:30,140 One. 244 00:16:30,140 --> 00:16:32,140 One. 245 00:16:32,140 --> 00:16:33,840 50. 246 00:16:33,840 --> 00:16:35,860 50. 247 00:16:35,860 --> 00:16:37,860 50. 248 00:16:37,860 --> 00:16:39,860 50. 249 00:16:39,860 --> 00:16:41,860 50. 250 00:16:41,860 --> 00:16:43,860 5. 251 00:16:43,860 --> 00:16:45,780 50. 252 00:16:45,980 --> 00:16:47,000 Valle. 253 00:16:47,000 --> 00:16:47,780 Venga. 254 00:16:47,780 --> 00:16:49,760 Vamos a hacer otra ecuación, 255 00:16:49,760 --> 00:16:51,660 pasamos la de 2º grado. 256 00:16:59,660 --> 00:17:01,660 Vamos a poner otra. 257 00:17:01,660 --> 00:17:03,660 Es que sería... 258 00:17:15,780 --> 00:17:18,660 Esa es la cuestión. 259 00:17:45,780 --> 00:17:48,660 Vamos a poner otra. 260 00:18:15,780 --> 00:18:18,660 Vamos a poner otra. 261 00:18:45,780 --> 00:18:47,780 Vamos a poner otra. 262 00:19:15,780 --> 00:19:17,780 Vamos a poner otra. 263 00:19:46,780 --> 00:19:48,040 Vamos a poner otra. 264 00:19:50,020 --> 00:19:51,620 Vamos a poner otra. 265 00:19:53,620 --> 00:19:55,120 Vamos a poner otra. 266 00:20:00,100 --> 00:20:01,640 Vamos a hacer otra. 267 00:20:02,820 --> 00:20:04,380 Vamos a hacer otra. 268 00:20:09,380 --> 00:20:10,860 Bueno. 269 00:20:10,860 --> 00:20:11,860 Ya lo tenemos. 270 00:20:12,500 --> 00:20:13,500 Vamos a poner otra. 271 00:20:13,500 --> 00:20:14,500 Vamos a poner otra. 272 00:20:30,500 --> 00:20:31,500 ¿Sí? 273 00:20:35,500 --> 00:20:36,500 No. 274 00:20:36,500 --> 00:20:37,500 No viene. 275 00:20:43,500 --> 00:21:07,660 El primer paso es quitar paréntesis, 2X más 10, menos X menos 3, igual a menos 7. 276 00:21:07,660 --> 00:21:12,780 Ese es el primer paso. 277 00:21:12,780 --> 00:21:14,780 El siguiente paso, transponer. 278 00:21:26,780 --> 00:21:28,780 Ahí estamos. 279 00:21:28,780 --> 00:21:29,780 Hemos transpuesto. 280 00:21:29,780 --> 00:21:33,780 El 10 pasa restando y el 3 pasa sumando. 281 00:21:33,780 --> 00:21:34,780 Simplificar. 282 00:21:34,780 --> 00:21:41,780 X igual a menos 14. 283 00:22:05,780 --> 00:22:06,780 ¿Está entendido? 284 00:22:16,780 --> 00:22:17,780 Cuatro pasos. 285 00:22:22,780 --> 00:22:27,780 Quitar paréntesis, transponer, simplificar y despejar. 286 00:22:28,780 --> 00:22:35,780 Bueno, pues vamos a por la secuación en el segundo grado. 287 00:22:42,780 --> 00:22:43,780 Vamos a ver. 288 00:22:58,780 --> 00:22:59,780 Vamos a por el segundo grado. 289 00:23:12,780 --> 00:23:13,780 Vamos a por el tercer grado. 290 00:23:27,780 --> 00:23:28,780 Bien. 291 00:23:51,780 --> 00:23:54,780 Entonces, la secuación en el segundo grado tiene esta forma. 292 00:23:54,780 --> 00:23:55,780 Vamos a poner aquí. 293 00:23:55,780 --> 00:23:56,780 Voy a poner aquí. 294 00:23:57,780 --> 00:24:03,780 A por X al cuadrado, más B por X, más C, igual a cero. 295 00:24:03,780 --> 00:24:06,780 Esta es la secuación que vamos a tener que resolver. 296 00:24:08,780 --> 00:24:09,780 Esta. 297 00:24:09,780 --> 00:24:11,780 Una secuación en el segundo grado. 298 00:24:11,780 --> 00:24:13,780 Donde A es distinto de cero, claro. 299 00:24:13,780 --> 00:24:14,780 Si no, sería de primer grado. 300 00:24:14,780 --> 00:24:16,780 A es distinto de cero, siempre. 301 00:24:17,780 --> 00:24:18,780 B sí puede ser cero. 302 00:24:18,780 --> 00:24:19,780 Y C también. 303 00:24:19,780 --> 00:24:21,780 La incógnita es la X. 304 00:24:22,780 --> 00:24:24,780 Lo que debemos calcular. 305 00:24:37,780 --> 00:24:39,780 Entonces, por ejemplo, en la ecuación. 306 00:24:46,780 --> 00:24:47,780 Tres X al cuadrado. 307 00:24:52,780 --> 00:24:57,780 Menos cinco X, más dos, igual a cero. 308 00:24:58,780 --> 00:24:59,780 ¿Cuánto vale A? 309 00:25:00,780 --> 00:25:02,780 Lo que tenemos que hacer es saber cuánto vale A. 310 00:25:03,780 --> 00:25:08,780 Si A vale tres, ¿cuánto vale B? 311 00:25:10,780 --> 00:25:12,780 B vale menos cinco. 312 00:25:14,780 --> 00:25:15,780 ¿Y C? 313 00:25:16,780 --> 00:25:17,780 ¿Cuánto vale C? 314 00:25:19,780 --> 00:25:20,780 Dos. 315 00:25:21,780 --> 00:25:24,780 Lo primero que tenemos que saber es identificar cuáles son los coeficientes. 316 00:25:25,780 --> 00:25:29,780 En esta ecuación, A vale tres, B vale menos cinco y C vale dos. 317 00:25:32,780 --> 00:25:36,780 Y ahora vamos a ver cómo se resuelve. 318 00:25:52,780 --> 00:25:53,780 Bien. 319 00:26:09,780 --> 00:26:12,780 Vamos a ver, aquí tenemos la ecuación y la formulita. 320 00:26:14,780 --> 00:26:15,780 Que vamos a tener que utilizar. 321 00:26:18,780 --> 00:26:19,780 Esta sea la expresión. 322 00:26:21,780 --> 00:26:22,780 Nuestra ecuación de segundo grado. 323 00:26:22,780 --> 00:26:24,780 AX al cuadrado más la X más C igual a cero. 324 00:26:25,780 --> 00:26:26,780 Y nuestra fórmula. 325 00:26:27,780 --> 00:26:28,780 Cuatro por A por C. 326 00:26:28,780 --> 00:26:29,780 Esto está multiplicando. 327 00:26:29,780 --> 00:26:30,780 Cuatro por A por C. 328 00:26:31,780 --> 00:26:32,780 Partido dos por A. 329 00:26:33,780 --> 00:26:34,780 Esta fórmula sería la siguiente. 330 00:26:35,780 --> 00:26:38,780 X es igual a menos B. 331 00:26:40,780 --> 00:26:42,780 Más menos la raíz cuadrada. 332 00:26:44,780 --> 00:26:45,780 De B al cuadrado. 333 00:26:46,780 --> 00:26:49,780 Menos cuatro por A por C. 334 00:26:50,780 --> 00:26:53,780 Dividido dos por A. 335 00:26:55,780 --> 00:26:56,780 Esa es la fórmula que vamos a aplicar. 336 00:26:57,780 --> 00:26:59,780 Para calcular nuestras X. 337 00:27:08,780 --> 00:27:09,780 Entonces. 338 00:27:10,780 --> 00:27:11,780 Vamos a... 339 00:27:14,780 --> 00:27:15,780 A ver un ejemplo. 340 00:27:16,780 --> 00:27:18,780 La ecuación de segundo grado tiene dos soluciones. 341 00:27:20,780 --> 00:27:21,780 Una doble o ninguna. 342 00:27:22,780 --> 00:27:24,780 Esta ecuación tiene dos soluciones. 343 00:27:26,780 --> 00:27:27,780 Tiene dos soluciones. 344 00:27:33,780 --> 00:27:34,780 Una doble. 345 00:27:36,780 --> 00:27:37,780 O ninguna. 346 00:27:39,780 --> 00:27:40,780 O ninguna. 347 00:27:41,780 --> 00:27:42,780 Si la raíz es negativa. 348 00:27:43,780 --> 00:27:44,780 No tiene soluciones. 349 00:27:44,780 --> 00:27:45,780 Vamos a ver ejemplos. 350 00:27:49,780 --> 00:27:50,780 Bueno. 351 00:28:17,780 --> 00:28:18,780 Bueno. 352 00:28:18,780 --> 00:28:19,780 Aquí una ecuación. 353 00:28:21,780 --> 00:28:23,780 Por ejemplo, X al cuadrado. 354 00:28:29,780 --> 00:28:30,780 Menos cinco X. 355 00:28:32,780 --> 00:28:33,780 Más seis. 356 00:28:34,780 --> 00:28:35,780 Igual a cero. 357 00:28:36,780 --> 00:28:37,780 Tenemos que resolver esa ecuación. 358 00:28:42,780 --> 00:28:44,780 Entonces, lo primero de todo va a ser... 359 00:28:45,780 --> 00:28:47,780 Saber cuánto vale la A, la B y la C. 360 00:28:48,780 --> 00:28:50,780 Entonces, ¿cuánto vale la A? 361 00:28:54,780 --> 00:28:55,780 ¿Cuánto vale la A? 362 00:28:57,780 --> 00:28:58,780 Pues uno. 363 00:28:59,780 --> 00:29:00,780 A vale uno. 364 00:29:01,780 --> 00:29:02,780 ¿Cuánto vale la B? 365 00:29:06,780 --> 00:29:08,780 Pues menos cinco. 366 00:29:10,780 --> 00:29:11,780 ¿Cuánto vale la C? 367 00:29:12,780 --> 00:29:13,780 Más seis. 368 00:29:19,780 --> 00:29:20,780 Vale. 369 00:29:21,780 --> 00:29:24,780 Ya que tenemos las letras, las vamos a introducir en la fórmula. 370 00:29:25,780 --> 00:29:27,780 Y vamos a ver cómo calculamos la X. 371 00:29:28,780 --> 00:29:29,780 Vamos a ir despacito. 372 00:29:30,780 --> 00:29:32,780 X es igual a menos B. 373 00:29:33,780 --> 00:29:34,780 A menos B. 374 00:29:35,780 --> 00:29:36,780 Pero B vale menos cinco. 375 00:29:38,780 --> 00:29:39,780 Menos B. 376 00:29:40,780 --> 00:29:41,780 La B vale menos cinco. 377 00:29:42,780 --> 00:29:43,780 Más, menos, la raíz cuadrada. 378 00:29:44,780 --> 00:29:45,780 De B al cuadrado. 379 00:29:46,780 --> 00:29:48,780 O sea, de menos cinco al cuadrado. 380 00:29:49,780 --> 00:29:50,780 Menos cuatro por A. 381 00:29:52,780 --> 00:29:53,780 Que es uno. 382 00:29:54,780 --> 00:29:55,780 Por C. 383 00:29:56,780 --> 00:29:57,780 Que es seis. 384 00:29:58,780 --> 00:29:59,780 Dividido. 385 00:30:01,780 --> 00:30:02,780 Dos por uno. 386 00:30:02,780 --> 00:30:03,780 Dividido. 387 00:30:05,780 --> 00:30:06,780 Dos por uno. 388 00:30:14,780 --> 00:30:18,780 Vale, pues ya tenemos las letras introducidas en la fórmula. 389 00:30:19,780 --> 00:30:20,780 Ahora ya tenemos que operar. 390 00:30:26,780 --> 00:30:27,780 Vamos a ver cuánto vale X. 391 00:30:28,780 --> 00:30:29,780 Me voy aquí y digo X es igual. 392 00:30:30,780 --> 00:30:31,780 Menos menos cinco. 393 00:30:32,780 --> 00:30:33,780 Pues cinco. 394 00:30:34,780 --> 00:30:36,780 Más, menos, la raíz cuadrada. 395 00:30:38,780 --> 00:30:39,780 De menor cinco al cuadrado. 396 00:30:40,780 --> 00:30:41,780 O sea, veinticinco. 397 00:30:44,780 --> 00:30:46,780 Menos cuatro por uno es cuatro. 398 00:30:47,780 --> 00:30:48,780 Por C es veinticuatro. 399 00:30:50,780 --> 00:30:51,780 Dividido. 400 00:30:53,780 --> 00:30:54,780 Dos. 401 00:30:55,780 --> 00:30:56,780 Igual. 402 00:30:57,780 --> 00:30:58,780 Seguimos. 403 00:31:00,780 --> 00:31:01,780 Esto sería cinco. 404 00:31:02,780 --> 00:31:04,780 Más, menos, la raíz cuadrada. 405 00:31:05,780 --> 00:31:06,780 De veinticinco menos veinticuatro. 406 00:31:07,780 --> 00:31:08,780 De uno. 407 00:31:09,780 --> 00:31:10,780 Dividido. 408 00:31:11,780 --> 00:31:12,780 Dos. 409 00:31:13,780 --> 00:31:14,780 Esto sería igual a cinco más menos. 410 00:31:15,780 --> 00:31:16,780 La raíz cuadrada de uno es uno. 411 00:31:19,780 --> 00:31:20,780 Dos. 412 00:31:21,780 --> 00:31:22,780 Y ahora aquí tengo dos soluciones. 413 00:31:23,780 --> 00:31:24,780 Cinco más uno seis. 414 00:31:25,780 --> 00:31:26,780 Aquí tengo dos soluciones. 415 00:31:27,780 --> 00:31:28,780 Cinco más uno. 416 00:31:29,780 --> 00:31:30,780 Dos. 417 00:31:31,780 --> 00:31:32,780 Y cinco. 418 00:31:33,780 --> 00:31:34,780 Menos uno. 419 00:31:35,780 --> 00:31:36,780 Dividido dos. 420 00:31:38,780 --> 00:31:39,780 Cinco más uno seis. 421 00:31:40,780 --> 00:31:41,780 Entre dos. 422 00:31:42,780 --> 00:31:43,780 Tres. 423 00:31:44,780 --> 00:31:45,780 Y cinco menos uno cuatro. 424 00:31:46,780 --> 00:31:47,780 Entre dos. 425 00:31:48,780 --> 00:31:49,780 Dos. 426 00:31:50,780 --> 00:31:51,780 O sea que la solución tres. 427 00:31:52,780 --> 00:31:53,780 Y dos. 428 00:31:54,780 --> 00:31:55,780 Ya tengo las soluciones de la ecuación. 429 00:31:56,780 --> 00:31:57,780 Tres y dos. 430 00:31:59,780 --> 00:32:00,780 El tres se cumple ¿no? 431 00:32:01,780 --> 00:32:02,780 Tres al cuadrado es nueve. 432 00:32:04,780 --> 00:32:05,780 Nueve menos quince más seis. 433 00:32:07,780 --> 00:32:08,780 Nueve menos quince más seis. 434 00:32:09,780 --> 00:32:10,780 Es igual a cero. 435 00:32:12,780 --> 00:32:13,780 Esa está bien. 436 00:32:16,780 --> 00:32:17,780 Y la otra ecuación. 437 00:32:18,780 --> 00:32:19,780 La otra solución. 438 00:32:20,780 --> 00:32:21,780 El dos. 439 00:32:23,780 --> 00:32:24,780 Vamos a ver si cumple. 440 00:32:27,780 --> 00:32:28,780 Dos al cuadrado. 441 00:32:29,780 --> 00:32:30,780 Se atendríamos dos al cuadrado. 442 00:32:32,780 --> 00:32:33,780 Menos cinco por dos. 443 00:32:34,780 --> 00:32:35,780 Más seis. 444 00:32:36,780 --> 00:32:37,780 Cuatro menos diez. 445 00:32:38,780 --> 00:32:39,780 Más seis. 446 00:32:40,780 --> 00:32:41,780 Sí es cero. 447 00:32:42,780 --> 00:32:43,780 Está bien también. 448 00:32:44,780 --> 00:32:45,780 La comprobación. 449 00:32:49,780 --> 00:32:51,780 Sustituimos los valores de la solución en la ecuación. 450 00:32:52,780 --> 00:32:53,780 Tiene que dártela. 451 00:32:54,780 --> 00:32:55,780 Luego esto será el procedimiento. 452 00:32:56,780 --> 00:32:57,780 ¿Se ha entendido? 453 00:33:00,780 --> 00:33:01,780 Aplicamos la fórmula. 454 00:33:02,780 --> 00:33:04,780 Primero tenemos que saber A, B y C. 455 00:33:05,780 --> 00:33:06,780 Vamos a ver otro ejemplo. 456 00:33:12,780 --> 00:33:13,780 Venga, vamos a ver otro ejemplo. 457 00:33:25,780 --> 00:33:26,780 X igual. 458 00:33:27,780 --> 00:33:28,780 X igual. 459 00:33:30,780 --> 00:33:31,780 Vamos a poner dos X al cuadrado. 460 00:33:33,780 --> 00:33:34,780 Dos X al cuadrado. 461 00:33:37,780 --> 00:33:38,780 Menos siete X. 462 00:33:39,780 --> 00:33:40,780 Más tres. 463 00:33:40,780 --> 00:33:41,780 Igual a cero. 464 00:33:44,780 --> 00:33:45,780 Bien, entonces lo primero. 465 00:33:46,780 --> 00:33:47,780 ¿Cuánto vale A, B y C? 466 00:33:48,780 --> 00:33:49,780 ¿Cuánto vale A? 467 00:33:52,780 --> 00:33:53,780 Dos. 468 00:33:53,780 --> 00:33:54,780 ¿Cuánto vale B? 469 00:33:54,780 --> 00:33:55,780 ¿Cuánto vale B? 470 00:33:57,780 --> 00:33:58,780 Menos siete. 471 00:33:58,780 --> 00:33:59,780 ¿Cuánto vale C? 472 00:34:01,780 --> 00:34:02,780 Tres. 473 00:34:02,780 --> 00:34:03,780 Ya tengo los valores. 474 00:34:04,780 --> 00:34:06,780 A dos, B menos siete y C tres. 475 00:34:07,780 --> 00:34:08,780 Y ahora tengo que aplicar 476 00:34:09,780 --> 00:34:10,780 a la fórmula. 477 00:34:15,780 --> 00:34:18,780 X es igual a menos B. 478 00:34:20,780 --> 00:34:22,780 A menos B, que es menos siete. 479 00:34:22,780 --> 00:34:24,780 Más menos la raíz cuadrada. 480 00:34:25,780 --> 00:34:26,780 De menos siete al cuadrado. 481 00:34:27,780 --> 00:34:28,780 O sea, de B al cuadrado. 482 00:34:29,780 --> 00:34:30,780 Menos cuatro. 483 00:34:31,780 --> 00:34:32,780 Por dos. 484 00:34:32,780 --> 00:34:33,780 Por tres. 485 00:34:34,780 --> 00:34:35,780 Dividido. 486 00:34:37,780 --> 00:34:38,780 Dos por A. 487 00:34:39,780 --> 00:34:40,780 Dos por dos. 488 00:34:42,780 --> 00:34:43,780 Venga. 489 00:34:43,780 --> 00:34:44,780 Pues ahora aquí vamos a seguir operando. 490 00:34:45,780 --> 00:34:46,780 X. 491 00:34:47,780 --> 00:34:48,780 Igual. 492 00:34:49,780 --> 00:34:50,780 Menos por menos más. 493 00:34:50,780 --> 00:34:51,780 A siete. 494 00:34:52,780 --> 00:34:54,780 Más menos la raíz cuadrada. 495 00:34:55,780 --> 00:34:56,780 Menos siete al cuadrado. 496 00:34:56,780 --> 00:34:57,780 Cuarenta y nueve. 497 00:34:58,780 --> 00:34:59,780 Menos. 498 00:35:00,780 --> 00:35:01,780 Veinticuatro. 499 00:35:02,780 --> 00:35:03,780 Cuatro por dos, ocho. 500 00:35:03,780 --> 00:35:04,780 Por tres, veinticuatro. 501 00:35:05,780 --> 00:35:06,780 Dividido. 502 00:35:07,780 --> 00:35:08,780 Cuatro. 503 00:35:09,780 --> 00:35:10,780 Y esto es igual. 504 00:35:11,780 --> 00:35:12,780 A siete. 505 00:35:12,780 --> 00:35:14,780 Más menos la raíz cuadrada. 506 00:35:15,780 --> 00:35:16,780 Cuarenta y nueve menos veinticuatro. 507 00:35:17,780 --> 00:35:18,780 Veinticinco. 508 00:35:18,780 --> 00:35:19,780 Veinticinco. 509 00:35:20,780 --> 00:35:21,780 Partido. 510 00:35:21,780 --> 00:35:22,780 Cuatro. 511 00:35:23,780 --> 00:35:26,780 Luego esto sería igual a siete más menos cinco. 512 00:35:27,780 --> 00:35:28,780 Raíz de veinticinco cinco. 513 00:35:29,780 --> 00:35:30,780 Partido cuatro. 514 00:35:31,780 --> 00:35:32,780 Y aquí tengo dos soluciones. 515 00:35:34,780 --> 00:35:35,780 Siete más cinco. 516 00:35:36,780 --> 00:35:37,780 Dividido cuatro. 517 00:35:39,780 --> 00:35:40,780 Y aquí tengo otra. 518 00:35:41,780 --> 00:35:42,780 Siete menos cinco. 519 00:35:43,780 --> 00:35:44,780 Dividido cuatro. 520 00:35:45,780 --> 00:35:47,780 Esto sería siete más cinco doce. 521 00:35:48,780 --> 00:35:49,780 Cuatro sería tres. 522 00:35:51,780 --> 00:35:54,780 Y esta sería dos cuartos. 523 00:35:55,780 --> 00:35:56,780 Que sería un medio. 524 00:35:59,780 --> 00:36:00,780 Un medio. 525 00:36:13,780 --> 00:36:14,780 ¿Se entiende? 526 00:36:19,780 --> 00:36:20,780 Vamos a ver otro ejemplo. 527 00:36:20,780 --> 00:36:23,780 Ahora vamos a ver un ejemplo donde sale las raíces. 528 00:36:34,780 --> 00:36:35,780 Vamos a ver otro ejemplo aquí. 529 00:36:36,780 --> 00:36:37,780 X al cuadrado. 530 00:36:41,780 --> 00:36:42,780 Menos cuatro X. 531 00:36:44,780 --> 00:36:45,780 Y menos cuatro X. 532 00:36:45,780 --> 00:36:46,780 Menos cuatro X. 533 00:36:48,780 --> 00:36:49,780 Más cuatro. 534 00:36:49,780 --> 00:36:50,780 Igual a cero. 535 00:36:50,780 --> 00:36:51,780 ¿Cuánto vale A? 536 00:36:52,780 --> 00:36:53,780 Uno. 537 00:36:53,780 --> 00:36:54,780 ¿Cuánto vale B? 538 00:36:54,780 --> 00:36:55,780 Menos cuatro. 539 00:36:55,780 --> 00:36:56,780 ¿Cuánto vale C? 540 00:36:57,780 --> 00:36:58,780 Cuatro. 541 00:36:59,780 --> 00:37:00,780 Venga. 542 00:37:00,780 --> 00:37:01,780 Entonces aplicamos la fórmula. 543 00:37:02,780 --> 00:37:05,780 X es igual a menos menos cuatro. 544 00:37:06,780 --> 00:37:08,780 Más menos la raíz cuadrada. 545 00:37:09,780 --> 00:37:11,780 De menos cuatro al cuadrado. 546 00:37:11,780 --> 00:37:12,780 Menos cuatro. 547 00:37:13,780 --> 00:37:14,780 Por una. 548 00:37:14,780 --> 00:37:15,780 Por cuatro. 549 00:37:16,780 --> 00:37:17,780 Dividido. 550 00:37:19,780 --> 00:37:20,780 Dos por uno. 551 00:37:21,780 --> 00:37:22,780 Lo que había aquí. 552 00:37:24,780 --> 00:37:25,780 X igual. 553 00:37:26,780 --> 00:37:27,780 Menos por menos. 554 00:37:28,780 --> 00:37:29,780 Menos por menos. 555 00:37:29,780 --> 00:37:30,780 Más. 556 00:37:30,780 --> 00:37:31,780 Cuatro. 557 00:37:31,780 --> 00:37:33,780 Más menos la raíz cuadrada. 558 00:37:34,780 --> 00:37:35,780 De menos cuatro al cuadrado. 559 00:37:35,780 --> 00:37:36,780 Dieciséis. 560 00:37:37,780 --> 00:37:38,780 Menos. 561 00:37:39,780 --> 00:37:40,780 Cuatro por una. 562 00:37:40,780 --> 00:37:41,780 Cuatro por una. 563 00:37:41,780 --> 00:37:42,780 Cuatro por cuatro. 564 00:37:42,780 --> 00:37:43,780 Dieciséis. 565 00:37:44,780 --> 00:37:45,780 Dividido. 566 00:37:46,780 --> 00:37:47,780 Dos. 567 00:37:48,780 --> 00:37:50,780 Luego esto es igual a cuatro. 568 00:37:50,780 --> 00:37:52,780 Más menos la raíz de cero. 569 00:37:52,780 --> 00:37:53,780 Dividido. 570 00:37:53,780 --> 00:37:54,780 Dos. 571 00:37:54,780 --> 00:37:56,780 Esto es igual a cuatro. 572 00:37:56,780 --> 00:37:57,780 Más menos cero. 573 00:37:57,780 --> 00:37:58,780 Dividido. 574 00:37:58,780 --> 00:37:59,780 Dos. 575 00:37:59,780 --> 00:38:01,780 O sea, esto es igual a cuatro dividido dos. 576 00:38:02,780 --> 00:38:03,780 Es igual a dos. 577 00:38:04,780 --> 00:38:05,780 Una raíz doble. 578 00:38:06,780 --> 00:38:07,780 Aquí tenemos una raíz. 579 00:38:08,780 --> 00:38:09,780 Una raíz. 580 00:38:10,780 --> 00:38:11,780 Doble. 581 00:38:13,780 --> 00:38:14,780 En el dos. 582 00:38:19,780 --> 00:38:20,780 La raíz de cero. 583 00:38:21,780 --> 00:38:22,780 Pues una raíz. 584 00:38:22,780 --> 00:38:23,780 Una solución. 585 00:38:23,780 --> 00:38:24,780 X igual a dos. 586 00:38:29,780 --> 00:38:30,780 Aquí tenemos una solución. 587 00:38:31,780 --> 00:38:32,780 Una solución. 588 00:38:34,780 --> 00:38:35,780 Doble. 589 00:38:40,780 --> 00:38:41,780 Una solución. 590 00:38:41,780 --> 00:38:42,780 Doble. 591 00:38:43,780 --> 00:38:44,780 X igual a dos. 592 00:38:45,780 --> 00:38:47,780 Vamos a ver un ejemplo que pasa si nos sale la raíz negativa. 593 00:39:02,780 --> 00:39:03,780 Por ejemplo. 594 00:39:03,780 --> 00:39:04,780 X al cuadrado. 595 00:39:08,780 --> 00:39:09,780 Más X. 596 00:39:10,780 --> 00:39:11,780 Más tres. 597 00:39:12,780 --> 00:39:13,780 Igual a cero. 598 00:39:14,780 --> 00:39:15,780 Entonces tengo que A es igual a uno. 599 00:39:16,780 --> 00:39:17,780 B es igual a uno. 600 00:39:18,780 --> 00:39:19,780 Y C es igual a tres. 601 00:39:21,780 --> 00:39:22,780 Voy a aplicar la forma aquí. 602 00:39:24,780 --> 00:39:26,780 X es igual a menos B. 603 00:39:40,780 --> 00:39:41,780 Y B es igual a menos C. 604 00:40:04,780 --> 00:40:05,780 X al cuadrado. 605 00:40:06,780 --> 00:40:07,780 Más X. 606 00:40:07,780 --> 00:40:08,780 Más tres. 607 00:40:08,780 --> 00:40:09,780 Igual a cero. 608 00:40:10,780 --> 00:40:11,780 A es igual a uno. 609 00:40:12,780 --> 00:40:13,780 B es igual a uno. 610 00:40:13,780 --> 00:40:14,780 Y C es igual a tres. 611 00:40:16,780 --> 00:40:17,780 Entonces. 612 00:40:17,780 --> 00:40:18,780 X es igual a menos B. 613 00:40:19,780 --> 00:40:20,780 O sea, a menos uno. 614 00:40:21,780 --> 00:40:22,780 Más menos la raíz cuadrada. 615 00:40:24,780 --> 00:40:25,780 De uno al cuadrado. 616 00:40:27,780 --> 00:40:28,780 Menos cuatro. 617 00:40:29,780 --> 00:40:30,780 Por A. 618 00:40:31,780 --> 00:40:32,780 Por C. 619 00:40:33,780 --> 00:40:34,780 Dividido. 620 00:40:36,780 --> 00:40:37,780 Dos por uno. 621 00:40:38,780 --> 00:40:39,780 Luego esto sería. 622 00:40:40,780 --> 00:40:41,780 Menos uno. 623 00:40:42,780 --> 00:40:43,780 Más menos la raíz cuadrada. 624 00:40:45,780 --> 00:40:46,780 De uno. 625 00:40:46,780 --> 00:40:47,780 Menos doce. 626 00:40:48,780 --> 00:40:49,780 Partido. 627 00:40:49,780 --> 00:40:50,780 Dos. 628 00:40:50,780 --> 00:40:51,780 Esto sería igual. 629 00:40:54,780 --> 00:40:55,780 A menos uno. 630 00:40:56,780 --> 00:40:57,780 Más menos la raíz cuadrada. 631 00:40:58,780 --> 00:40:59,780 De menos once. 632 00:41:00,780 --> 00:41:01,780 Partido. 633 00:41:01,780 --> 00:41:02,780 Dos. 634 00:41:03,780 --> 00:41:04,780 Pero la raíz cuadrada de menos once no existe. 635 00:41:04,780 --> 00:41:05,780 No existe. 636 00:41:09,780 --> 00:41:10,780 Por lo tanto. 637 00:41:11,780 --> 00:41:12,780 No hay solución. 638 00:41:16,780 --> 00:41:17,780 No hay solución real. 639 00:41:18,780 --> 00:41:19,780 No hay solución real. 640 00:41:26,780 --> 00:41:27,780 ¿Vale? 641 00:41:34,780 --> 00:41:35,780 La raíz negativa. 642 00:41:35,780 --> 00:41:36,780 Aquí. 643 00:41:37,780 --> 00:41:38,780 No existe. 644 00:41:38,780 --> 00:41:39,780 La raíz de un número negativo. 645 00:41:39,780 --> 00:41:40,780 Luego no hay solución. 646 00:41:54,780 --> 00:41:55,780 Venga. 647 00:41:55,780 --> 00:41:56,780 Voy a poner alguna. 648 00:41:56,780 --> 00:41:57,780 Para que hagáis. 649 00:42:04,780 --> 00:42:05,780 ¿Vale? 650 00:42:31,780 --> 00:42:32,780 Es. 651 00:42:34,780 --> 00:42:35,780 ¿Vale? 652 00:42:39,780 --> 00:42:40,780 Resolver eso. 653 00:42:45,780 --> 00:42:46,780 Este ya lo hemos hecho, ¿no? 654 00:42:49,780 --> 00:42:50,780 Este ya está hecho. 655 00:43:04,780 --> 00:43:05,780 Este. 656 00:43:13,780 --> 00:43:14,780 Este. 657 00:43:18,780 --> 00:43:19,780 Este. 658 00:43:34,780 --> 00:43:35,780 Este. 659 00:45:04,780 --> 00:45:32,780 Hello, everyone. 660 00:45:32,780 --> 00:45:57,780 My name is 661 00:49:28,780 --> 00:49:30,780 Let's start with this formula. 662 00:49:30,780 --> 00:49:35,780 a times x squared plus c equals 0. 663 00:49:36,780 --> 00:49:38,780 That is, b does not exist. 664 00:49:39,780 --> 00:49:41,780 b does not exist. 665 00:49:42,780 --> 00:49:45,780 You can also apply the formula, but well, b equals 0. 666 00:49:45,780 --> 00:49:47,780 b does not exist. 667 00:49:48,780 --> 00:49:51,780 So let's see how to solve these equations 668 00:49:52,780 --> 00:49:55,780 without using the formula, which is easier. 669 00:49:55,780 --> 00:49:57,780 I'm going to put an example here. 670 00:49:57,780 --> 00:49:59,780 For example, I can put here 671 00:50:00,780 --> 00:50:04,780 4x squared minus 2 equals 0. 672 00:50:05,780 --> 00:50:07,780 4x squared minus 2 equals 0. 673 00:50:08,780 --> 00:50:10,780 So what I'm going to do is 674 00:50:11,780 --> 00:50:13,780 clear the x squared. 675 00:50:13,780 --> 00:50:15,780 That is, the minus 2 676 00:50:15,780 --> 00:50:17,780 passes adding. 677 00:50:18,780 --> 00:50:20,780 4x squared is equal to 678 00:50:22,780 --> 00:50:24,780 Well, I was wrong. 679 00:50:25,780 --> 00:50:27,780 I did not want to put this. 680 00:50:28,780 --> 00:50:30,780 Let's 681 00:50:31,780 --> 00:50:33,780 modify. 682 00:50:35,780 --> 00:50:37,780 It's the other way around. I want to put this. 683 00:50:39,780 --> 00:50:43,780 2x squared minus 4 equals 0. 684 00:50:45,780 --> 00:50:47,780 So what are we going to do? 685 00:50:47,780 --> 00:50:49,780 Let's erase this from here. 686 00:50:51,780 --> 00:50:53,780 I'm going to put it up. 687 00:50:55,780 --> 00:50:57,780 Well, 688 00:50:57,780 --> 00:50:59,780 I don't know how to put it up. 689 00:51:00,780 --> 00:51:02,780 Come on, let's clear 690 00:51:02,780 --> 00:51:04,780 the x squared. 691 00:51:04,780 --> 00:51:06,780 That is, 2x squared 692 00:51:08,780 --> 00:51:10,780 is equal to 4. 693 00:51:10,780 --> 00:51:12,780 Because minus 4, we pass it to the other side 694 00:51:12,780 --> 00:51:14,780 adding. 695 00:51:14,780 --> 00:51:16,780 2x squared 696 00:51:16,780 --> 00:51:18,780 is equal to 4. 697 00:51:18,780 --> 00:51:20,780 Well, 698 00:51:20,780 --> 00:51:22,780 let's clear the x squared. 699 00:51:22,780 --> 00:51:24,780 x squared is equal to 4. 700 00:51:24,780 --> 00:51:26,780 So, 701 00:51:26,780 --> 00:51:28,780 what is x squared equal to? 702 00:51:28,780 --> 00:51:30,780 4 divided by 2. 703 00:51:30,780 --> 00:51:32,780 It's multiplying by 2, 704 00:51:32,780 --> 00:51:34,780 so it passes dividing. 705 00:51:34,780 --> 00:51:36,780 Then, this is equal to 2. 706 00:51:36,780 --> 00:51:38,780 x squared 707 00:51:38,780 --> 00:51:40,780 is equal to 2. 708 00:51:42,780 --> 00:51:44,780 x is equal to 709 00:51:44,780 --> 00:51:46,780 minus square root of 2. 710 00:51:46,780 --> 00:51:48,780 These are the solutions. 711 00:51:48,780 --> 00:51:50,780 I'm going to put 712 00:51:50,780 --> 00:51:52,780 another example 713 00:51:52,780 --> 00:51:54,780 that is 714 00:51:54,780 --> 00:51:56,780 exact 715 00:51:56,780 --> 00:51:58,780 so you can see it. 716 00:52:08,780 --> 00:52:10,780 There. 717 00:52:10,780 --> 00:52:12,780 4x squared minus 16 718 00:52:12,780 --> 00:52:14,780 is equal to 0. 719 00:52:14,780 --> 00:52:16,780 Let's go step by step. 720 00:52:16,780 --> 00:52:18,780 First, we clear 721 00:52:18,780 --> 00:52:20,780 the number ac 722 00:52:20,780 --> 00:52:22,780 to the right. 723 00:52:22,780 --> 00:52:24,780 4x squared 724 00:52:24,780 --> 00:52:26,780 is equal to 16. 725 00:52:26,780 --> 00:52:28,780 This is the first step. 726 00:52:28,780 --> 00:52:30,780 We pass the number 727 00:52:30,780 --> 00:52:32,780 to the right. 728 00:52:32,780 --> 00:52:34,780 It has to be positive, otherwise it's not valid. 729 00:52:34,780 --> 00:52:36,780 We clear the x. 730 00:52:36,780 --> 00:52:38,780 Second, x squared is equal 731 00:52:38,780 --> 00:52:40,780 to 16 divided by 4. 732 00:52:40,780 --> 00:52:42,780 This passes dividing. 733 00:52:42,780 --> 00:52:44,780 This is equal 734 00:52:44,780 --> 00:52:46,780 to 4. 735 00:52:48,780 --> 00:52:50,780 So, x squared 736 00:52:50,780 --> 00:52:52,780 is equal to 4. 737 00:52:56,780 --> 00:52:58,780 The third step 738 00:52:58,780 --> 00:53:00,780 is that 739 00:53:00,780 --> 00:53:02,780 x is equal to 740 00:53:02,780 --> 00:53:04,780 plus or minus 741 00:53:04,780 --> 00:53:06,780 square root of 4. 742 00:53:06,780 --> 00:53:08,780 Plus or minus square root of 4. 743 00:53:08,780 --> 00:53:10,780 It's plus 744 00:53:10,780 --> 00:53:12,780 or minus 2. 745 00:53:12,780 --> 00:53:14,780 These are the solutions. 746 00:53:14,780 --> 00:53:16,780 x is equal to 747 00:53:16,780 --> 00:53:18,780 x1 is equal to 2 748 00:53:18,780 --> 00:53:20,780 and x2 is equal to minus 2. 749 00:53:26,780 --> 00:53:28,780 There. 750 00:53:28,780 --> 00:53:30,780 We're going to apply the same procedure. 751 00:53:30,780 --> 00:53:32,780 Let's see another example. 752 00:53:56,780 --> 00:53:58,780 For example, 753 00:53:58,780 --> 00:54:00,780 5 754 00:54:00,780 --> 00:54:02,780 x squared 755 00:54:02,780 --> 00:54:04,780 minus... 756 00:54:08,780 --> 00:54:10,780 Not 5. 757 00:54:10,780 --> 00:54:12,780 Let's put 758 00:54:12,780 --> 00:54:14,780 2. 759 00:54:22,780 --> 00:54:24,780 Let's put 2. 760 00:54:24,780 --> 00:54:26,780 2x squared 761 00:54:26,780 --> 00:54:28,780 minus 50 762 00:54:28,780 --> 00:54:30,780 is equal to 0. 763 00:54:30,780 --> 00:54:32,780 2x squared minus 50 is equal to 0. 764 00:54:32,780 --> 00:54:34,780 First, let's pass the number 765 00:54:34,780 --> 00:54:36,780 to the right. 766 00:54:36,780 --> 00:54:38,780 2x squared 767 00:54:38,780 --> 00:54:40,780 is equal to 50. 768 00:54:40,780 --> 00:54:42,780 It's subtracting. 769 00:54:42,780 --> 00:54:44,780 Next step. 770 00:54:44,780 --> 00:54:46,780 This is the first one. 771 00:54:46,780 --> 00:54:48,780 2 passes dividing. 772 00:54:48,780 --> 00:54:50,780 x squared is equal to 773 00:54:50,780 --> 00:54:52,780 50 divided by 2 774 00:54:52,780 --> 00:54:54,780 is equal to 25. 775 00:54:54,780 --> 00:54:56,780 x squared is equal to 25. 776 00:55:00,780 --> 00:55:02,780 And now, 777 00:55:02,780 --> 00:55:04,780 the third step 778 00:55:04,780 --> 00:55:06,780 is that x 779 00:55:06,780 --> 00:55:08,780 is equal to 780 00:55:08,780 --> 00:55:10,780 plus or minus square root of 25. 781 00:55:12,780 --> 00:55:14,780 We always have to do the same steps. 782 00:55:14,780 --> 00:55:16,780 x is equal to plus or minus square root of 25. 783 00:55:16,780 --> 00:55:18,780 That is, x is equal to 784 00:55:18,780 --> 00:55:20,780 plus or minus 5. 785 00:55:22,780 --> 00:55:24,780 This is a way of solving 786 00:55:24,780 --> 00:55:26,780 this type of equation. 787 00:55:28,780 --> 00:55:30,780 If we apply the formula, 788 00:55:30,780 --> 00:55:32,780 it would be 789 00:55:32,780 --> 00:55:34,780 2 790 00:55:34,780 --> 00:55:36,780 b would be 0 791 00:55:36,780 --> 00:55:38,780 and c would be minus 50. 792 00:55:40,780 --> 00:55:42,780 But it will take 793 00:55:42,780 --> 00:55:44,780 a lot longer. 794 00:55:44,780 --> 00:55:46,780 You pass the number, 795 00:55:46,780 --> 00:55:48,780 divide by the coefficient 796 00:55:48,780 --> 00:55:50,780 of x squared 797 00:55:50,780 --> 00:55:52,780 and calculate the square root. 798 00:55:52,780 --> 00:55:54,780 It's an easy formula to do. 799 00:55:56,780 --> 00:55:58,780 Do you understand? 800 00:56:00,780 --> 00:56:02,780 Let's do one. 801 00:56:02,780 --> 00:56:04,780 We will do one. 802 00:56:04,780 --> 00:56:06,780 Let's see. 803 00:56:06,780 --> 00:56:08,780 25 divided by 2 is equal to 804 00:56:08,780 --> 00:56:10,780 5 x squared minus 100 805 00:56:10,780 --> 00:56:12,780 which is equal to 0. 806 00:56:12,780 --> 00:56:14,780 Let's do this one. 807 00:56:14,780 --> 00:56:16,780 x is equal to minus square root of 808 00:56:16,780 --> 00:56:18,780 25. 809 00:56:20,780 --> 00:56:22,780 x is equal to minus square root of 25. 810 00:56:24,780 --> 00:56:26,780 So, we have 811 00:56:26,780 --> 00:56:28,780 x is equal to minus 812 00:56:28,780 --> 00:56:30,780 5 x squared minus 100 813 00:56:30,780 --> 00:56:32,780 which is equal to 0. 814 00:56:32,780 --> 00:56:34,780 Let's do this one. 815 00:56:40,780 --> 00:56:42,780 No, sorry. Wait, wait, wait. 816 00:56:44,780 --> 00:56:46,780 So that it comes out exact. 817 00:56:46,780 --> 00:56:48,780 I'm going to put a... 818 00:56:50,780 --> 00:56:52,780 So that it comes out exact. 819 00:56:52,780 --> 00:56:54,780 Here it has to be 820 00:56:54,780 --> 00:56:56,780 a 4. 821 00:56:56,780 --> 00:56:58,780 So that it comes out exact. 822 00:57:00,780 --> 00:57:02,780 So that it comes out exact. 823 00:57:02,780 --> 00:57:04,780 . 824 00:57:04,780 --> 00:57:06,780 . 825 00:57:06,780 --> 00:57:08,780 . 826 00:57:08,780 --> 00:57:10,780 . 827 00:57:10,780 --> 00:57:12,780 . 828 00:57:12,780 --> 00:57:14,780 . 829 00:57:14,780 --> 00:57:16,780 . 830 00:57:16,780 --> 00:57:18,780 . 831 00:57:18,780 --> 00:57:20,780 . 832 00:57:20,780 --> 00:57:22,780 . 833 00:57:22,780 --> 00:57:24,780 . 834 00:57:24,780 --> 00:57:26,780 . 835 00:57:26,780 --> 00:57:28,780 . 836 00:57:28,780 --> 00:57:30,780 . 837 00:57:30,780 --> 00:57:32,780 . 838 00:57:32,780 --> 00:57:34,780 . 839 00:57:36,780 --> 00:57:38,780 . 840 00:57:38,780 --> 00:57:40,780 . 841 00:57:40,780 --> 00:57:42,780 . 842 00:57:42,780 --> 00:57:44,780 . 843 00:57:44,780 --> 00:57:46,780 . 844 00:57:46,780 --> 00:57:48,780 . 845 00:57:48,780 --> 00:57:50,780 . 846 00:57:50,780 --> 00:57:52,780 . 847 00:57:52,780 --> 00:57:54,780 . 848 00:57:54,780 --> 00:57:56,780 . 849 00:57:56,780 --> 00:57:58,780 . 850 00:57:58,780 --> 00:58:00,780 . 851 00:58:02,780 --> 00:58:04,780 . 852 00:58:04,780 --> 00:58:06,780 . 853 00:58:06,780 --> 00:58:08,780 . 854 00:58:08,780 --> 00:58:10,780 . 855 00:58:10,780 --> 00:58:12,780 . 856 00:58:12,780 --> 00:58:14,780 . 857 00:58:14,780 --> 00:58:16,780 . 858 00:58:16,780 --> 00:58:18,780 . 859 00:58:18,780 --> 00:58:20,780 . 860 00:58:20,780 --> 00:58:22,780 . 861 00:58:22,780 --> 00:58:24,780 . 862 00:58:24,780 --> 00:58:26,780 . 863 00:58:26,780 --> 00:58:28,780 . 864 00:58:28,780 --> 00:58:30,780 . 865 00:58:30,780 --> 00:58:32,780 . 866 00:58:32,780 --> 00:58:34,780 . 867 00:58:34,780 --> 00:58:36,780 . 868 00:58:38,780 --> 00:58:40,780 . 869 00:58:40,780 --> 00:58:42,780 . 870 00:58:42,780 --> 00:58:44,780 . 871 00:58:44,780 --> 00:58:46,780 . 872 00:58:46,780 --> 00:58:48,780 . 873 00:58:48,780 --> 00:58:50,780 . 874 00:58:50,780 --> 00:58:52,780 . 875 00:58:52,780 --> 00:58:54,780 . 876 00:58:56,780 --> 00:58:58,780 . 877 00:58:58,780 --> 00:59:00,780 . 878 00:59:00,780 --> 00:59:02,780 . 879 00:59:02,780 --> 00:59:04,780 . 880 00:59:04,780 --> 00:59:06,780 . 881 00:59:06,780 --> 00:59:08,780 . 882 00:59:08,780 --> 00:59:10,780 . 883 00:59:10,780 --> 00:59:12,780 . 884 00:59:12,780 --> 00:59:14,780 . 885 00:59:14,780 --> 00:59:16,780 . 886 00:59:16,780 --> 00:59:18,780 . 887 00:59:18,780 --> 00:59:20,780 . 888 00:59:20,780 --> 00:59:22,780 . 889 00:59:24,780 --> 00:59:26,780 . 890 00:59:26,780 --> 00:59:28,780 . 891 00:59:28,780 --> 00:59:30,780 . 892 00:59:30,780 --> 00:59:32,780 . 893 00:59:32,780 --> 00:59:34,780 . 894 00:59:34,780 --> 00:59:36,780 . 895 00:59:36,780 --> 00:59:38,780 . 896 00:59:38,780 --> 00:59:40,780 . 897 00:59:40,780 --> 00:59:42,780 . 898 00:59:42,780 --> 00:59:44,780 . 899 00:59:44,780 --> 00:59:46,780 . 900 00:59:46,780 --> 00:59:48,780 . 901 00:59:48,780 --> 00:59:50,780 . 902 00:59:50,780 --> 00:59:52,780 . 903 00:59:54,780 --> 00:59:56,780 . 904 00:59:56,780 --> 00:59:58,780 . 905 00:59:58,780 --> 01:00:00,780 . 906 01:00:00,780 --> 01:00:02,780 . 907 01:00:02,780 --> 01:00:04,780 . 908 01:00:04,780 --> 01:00:06,780 . 909 01:00:06,780 --> 01:00:08,780 . 910 01:00:08,780 --> 01:00:10,780 . 911 01:00:10,780 --> 01:00:12,780 . 912 01:00:12,780 --> 01:00:14,780 . 913 01:00:14,780 --> 01:00:16,780 . 914 01:00:16,780 --> 01:00:18,780 . 915 01:00:18,780 --> 01:00:20,780 . 916 01:00:24,780 --> 01:00:26,780 . 917 01:00:26,780 --> 01:00:28,780 . 918 01:00:28,780 --> 01:00:30,780 . 919 01:00:30,780 --> 01:00:32,780 . 920 01:00:32,780 --> 01:00:34,780 . 921 01:00:34,780 --> 01:00:36,780 . 922 01:00:36,780 --> 01:00:38,780 . 923 01:00:38,780 --> 01:00:40,780 . 924 01:00:40,780 --> 01:00:42,780 . 925 01:00:42,780 --> 01:00:44,780 . 926 01:00:44,780 --> 01:00:46,780 . 927 01:00:46,780 --> 01:00:48,780 . 928 01:00:50,780 --> 01:00:52,780 . 929 01:00:52,780 --> 01:00:54,780 . 930 01:00:54,780 --> 01:00:56,780 . 931 01:00:56,780 --> 01:00:58,780 . 932 01:00:58,780 --> 01:01:00,780 . 933 01:01:00,780 --> 01:01:02,780 . 934 01:01:02,780 --> 01:01:04,780 . 935 01:01:04,780 --> 01:01:06,780 . 936 01:01:06,780 --> 01:01:08,780 . 937 01:01:08,780 --> 01:01:10,780 . 938 01:01:10,780 --> 01:01:12,780 . 939 01:01:12,780 --> 01:01:14,780 . 940 01:01:16,780 --> 01:01:18,780 . 941 01:01:18,780 --> 01:01:20,780 . 942 01:01:20,780 --> 01:01:22,780 . 943 01:01:22,780 --> 01:01:24,780 . 944 01:01:24,780 --> 01:01:26,780 . 945 01:01:26,780 --> 01:01:28,780 . 946 01:01:28,780 --> 01:01:30,780 . 947 01:01:30,780 --> 01:01:32,780 . 948 01:01:32,780 --> 01:01:34,780 . 949 01:01:34,780 --> 01:01:36,780 . 950 01:01:36,780 --> 01:01:38,780 . 951 01:01:38,780 --> 01:01:40,780 . 952 01:01:40,780 --> 01:01:42,780 . 953 01:01:44,780 --> 01:01:46,780 . 954 01:01:46,780 --> 01:01:48,780 . 955 01:01:48,780 --> 01:01:50,780 . 956 01:01:50,780 --> 01:01:52,780 . 957 01:01:52,780 --> 01:01:54,780 . 958 01:01:54,780 --> 01:01:56,780 . 959 01:01:56,780 --> 01:01:58,780 . 960 01:01:58,780 --> 01:02:00,780 . 961 01:02:00,780 --> 01:02:02,780 . 962 01:02:02,780 --> 01:02:04,780 . 963 01:02:04,780 --> 01:02:06,780 . 964 01:02:06,780 --> 01:02:08,780 .