Question

5X² - 90 = 10 + 4x ayudaaaaa :v​

Answer 1

Respuesta:

   $x = \frac{2+6\sqrt{14} }{5}$     ;       $x = \frac{2-6\sqrt{14} }{5}$

Explicación paso a paso:

5X² - 90 = 10 + 4x

$5x^{2} - 4x -90-10 = 0$

$5x^{2} -4x-100 = 0$

$\frac{5x^{2} }{5} - \frac{4x}{5} - \frac{100}{5} = \frac{0}{5}$

$x^{2} - \frac{4}{5} x = 20$

Resolvemos la ecuación completando cuadrados.

$x^{2} - \frac{4}{5 }x +( \frac{\frac{4}{5} }{2})^{2} = 20 +( \frac{\frac{4}{5} }{2} )^{2}$

$x^{2} -\frac{4}{5} x+ (\frac{4}{10})^{2} = 20 + (\frac{4}{10})^{2}$

$(x - \frac{4}{10} )^{2} = 20 + \frac{16}{100}$

$(x - \frac{4}{10} )^{2} = \frac{2016}{100}$

Buscamos raíz cuadrada en ambos miembros:          

$\sqrt{( x - \frac{4}{10} )^{2} } =$  ±  $\sqrt{\frac{2016}{100} }$

$( x - \frac{4}{10}) =$  ±   $\sqrt{\frac{144*14}{100} }$

$x - \frac{4}{10} =$ ±     $\frac{12}{10}\sqrt{14}$

$x = \frac{4}{10}$ ±    $\frac{12}{10\sqr} } \sqrt{14}$  

$x = \frac{4+12\sqrt{14} }{10} = \frac{2+6\sqrt{14} }{5}$

$x =\frac{4-12\sqrt{14} }{10} =\frac{2-6\sqrt{14} }{5}$