# How do you solve the quadratic -4-2p^2=-40 using any method?

May 3, 2017

$p = - 3 \sqrt{2} \textcolor{w h i t e}{\text{XX")orcolor(white)("XX}} p = + 3 \sqrt{2}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} - 4 - 2 {p}^{2} = - 40$

Simplify by multiplying everything on both sides by $\left(- 1\right)$
$\textcolor{w h i t e}{\text{XXX}} 4 + 2 {p}^{2} = 40$

Subtract $4$ from both sides
$\textcolor{w h i t e}{\text{XXX}} 2 {p}^{2} = 36$

Divide both sides by $2$
$\textcolor{w h i t e}{\text{XXX}} {p}^{2} = 18$

Take the square root (giving both a positive and a negative possible solution)
$\textcolor{w h i t e}{\text{XXX}} p = \pm \sqrt{18} = \pm 3 \sqrt{2}$