# How do you solve the equation 2(x^2-5)=-x^2-1?

Jun 8, 2017

$x = \pm \sqrt{3}$

#### Explanation:

Multiply the $2$ through on the left hand side:

$2 \left({x}^{2} - 5\right) = - {x}^{2} - 1$

$2 {x}^{2} - 10 = - {x}^{2} - 1$

Add $\textcolor{red}{{x}^{2}}$ and $\textcolor{b l u e}{10}$ to both sides

$2 {x}^{2} \textcolor{red}{+ {x}^{2}} - 10 \textcolor{b l u e}{+ 10} = - {x}^{2} \textcolor{red}{+ {x}^{2}} - 1 \textcolor{b l u e}{+ 10}$

$3 {x}^{2} = 9$

Divide both sides by $3$

$\frac{3 {x}^{2}}{\textcolor{red}{3}} = \frac{9}{\textcolor{red}{3}}$

${x}^{2} = 3$

Take $\sqrt{\textcolor{w h i t e}{a a}}$ of both sides

color(red)(sqrt(color(black)(x^2))=color(red)(+-sqrt(color(black)(3))

$x = \pm \sqrt{3}$