# How do you solve the equation a-2x^2=-5?

Aug 18, 2017

See a solution process below.

#### Explanation:

Assuming you are trying to solve for $x$:

First, subtract $\textcolor{red}{a}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$- \textcolor{red}{a} + a - 2 {x}^{2} = - \textcolor{red}{a} - 5$

$0 - 2 {x}^{2} = - a - 5$

$- 2 {x}^{2} = - a - 5$

Next, divide each side of the equation by $\textcolor{red}{- 2}$ to isolate ${x}^{2}$ while keeping the equation balanced:

$\frac{- 2 {x}^{2}}{\textcolor{red}{- 2}} = \frac{- a - 5}{\textcolor{red}{- 2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} {x}^{2}}{\cancel{\textcolor{red}{- 2}}} = \frac{- a}{-} 2 + \frac{- 5}{-} 2$

${x}^{2} = \frac{a}{2} + \frac{5}{2}$

${x}^{2} = \frac{a + 5}{2}$

Now, take the square root of each side of the equation to solve for $x$ while keeping the equation balanced. Remember the square root of a number produces a positive and negative result:

$\sqrt{{x}^{2}} = \pm \sqrt{\frac{a + 5}{2}}$

$x = \pm \sqrt{\frac{a + 5}{2}}$