# How do you solve x^2=16 using the quadratic formula?

Jan 5, 2017

(see below for solution using quadratic formula)
$\textcolor{w h i t e}{\text{XXX}} x = \pm 4$

#### Explanation:

Rewriting ${x}^{2} = 16$ into explicit standard quadratic form:
$\textcolor{w h i t e}{\text{XXX")color(red)1x^2+color(blue)0x+color(green)(} \left(- 16\right)} = 0$

The quadratic formula tells us that a quadratic equation with the form:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{a} {x}^{2} + \textcolor{b l u e}{b} x + \textcolor{g r e e n}{c} = 0$
has solutions:
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - 4 \cdot \textcolor{red}{a} \cdot \textcolor{g r e e n}{c}}}{2 \cdot \textcolor{red}{a}}$

Our (standardized) quadratic has
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{a} = \textcolor{red}{1}$
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{b} = \textcolor{b l u e}{0}$
$\textcolor{w h i t e}{\text{XXX")color(green)c=color(green)(} \left(- 16\right)}$

So its solutions are
color(white)("XXX")x=(color(blue)0+-sqrt(color(blue)0^2-4 * color(red)1 * color(green)(""(-16))))/(2 * color(red)1

$\textcolor{w h i t e}{\text{XXXX}} = \pm \frac{\sqrt{64}}{2}$

$\textcolor{w h i t e}{\text{XXXX}} = \pm \frac{8}{2}$

$\textcolor{w h i t e}{\text{XXXX}} = \pm 4$