# How do you solve  x - 6 = -x^2 ?

Mar 5, 2018

See a solution process below:

#### Explanation:

First, put the equation in standard quadratic form:

$x - 6 = - {x}^{2}$

$\textcolor{red}{{x}^{2}} + x - 6 = \textcolor{red}{{x}^{2}} - {x}^{2}$

${x}^{2} + x - 6 = 0$

$\left(x + 3\right) \left(x - 2\right) = 0$

Now, solve each term on the left for $0$:

Solution 1:

$x + 3 = 0$

$x + 3 - \textcolor{red}{3} = 0 - \textcolor{red}{3}$

$x + 0 = - 3$

$x = - 3$

Solution 2:

$x - 2 = 0$

$x - 2 + \textcolor{red}{2} = 0 + \textcolor{red}{2}$

$x - 0 = 2$

$x = 2$

The Solution Is:

$x = \left\{- 3 , 2\right\}$