Question

matematicas
$10x {}^{2} + 7x - 12 = 0$

Answer 1

completo cuadrados no voy a usar bhaskara
$10 {x}^{2} + 7x - 12 = 0 \\ \\ 10( {x}^{2} + \frac{7}{10} x - \frac{12}{10} ) = 0 \\ \\ x {}^{2} + \frac{7}{10} x - \frac{6}{5} = 0 \\ \\ (x + \frac{7}{20} {)}^{2} - \frac{49}{400} - \frac{6}{5} = 0 \\ \\ (x + \frac{7}{20} {)}^{2} - \frac{529}{400} = 0 \\ \\ ( {x + \frac{7}{20}) }^{2} = \frac{529}{400} \\ \\ \sqrt{( {x + \frac{7}{20}) }^{2} } = \sqrt{ \frac{529}{400} } \\ \\ |x + \frac{7}{20} | = \frac{23}{20}$

ahora por definición de modulo
$|x + \frac{7}{20} | = \frac{23}{20}$
--
$x + \frac{7}{20 } = \frac{23}{20} \\ \\ x = \frac{23}{2 0} - \frac{7}{20} \\ \\ x = \frac{16}{20} = \frac{4}{5}$

"O"

$x + \frac{7}{20} = - \frac{23}{20} \\ \\ x = - \frac{23}{20} - \frac{7}{20 } \\ \\ x = - \frac{30}{20} = - \frac{3}{2}$

Solución: X=-3/2 "o" X=4/5

PD: si metes estos valores en la ecuación tiene que dar cero