# How do you solve -5x^2=-500?

Jul 26, 2016

$x = 10$

#### Explanation:

This is a good example of how operations can act on both sides of an equation in order to simplify and find the value of a variable.

I'll work this out showing each step:
$- 5 {x}^{2} = - 500$

$\left(\frac{1}{-} 5\right) \left(- 5 {x}^{2}\right) = - 500 \left(\frac{1}{-} 5\right)$

${x}^{2} = 100$

$\sqrt{{x}^{2}} = \sqrt{100}$

$x = 10$

Jul 26, 2016

$x = \pm 10$

#### Explanation:

Given:$\text{ } \textcolor{b r o w n}{- 5 {x}^{2} = - 500}$

To make $- 5 {x}^{2}$ positive multiply both sides by (-1)

$\text{ } \textcolor{b r o w n}{5 {x}^{2} = 500}$

Divide both sides by $\textcolor{b l u e}{5}$ turning the 5 in $5 {x}^{2}$ into 1

$\text{ } \textcolor{b r o w n}{\frac{5}{\textcolor{b l u e}{5}} \times {x}^{2} = \frac{500}{\textcolor{b l u e}{5}}}$

$\text{ } \textcolor{b r o w n}{{x}^{2} = 100}$

Square root both sides

$\text{ } \textcolor{b r o w n}{\sqrt{{x}^{2}} = \sqrt{100}}$

$\text{ } \textcolor{g r e e n}{x = \pm 10}$