# How do you solve x^2-175=0 using the quadratic formula?

Jul 25, 2016

$x = \pm 5 \sqrt{7}$

#### Explanation:

The quadratic formula for an equation in the form:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{a} {x}^{2} \textcolor{b l u e}{+ b} x + \textcolor{g r e e n}{c} = 0$
gives us the solutions:
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{\textcolor{b l u e}{b} - 4 \left(\textcolor{red}{a} \textcolor{g r e e n}{c}\right)}}{2 \textcolor{red}{a}}$

${x}^{2} - 175 = 0$ is equivalent to
$\textcolor{w h i t e}{\text{XXX")color(red)(1)x^2+color(blue)(0)x+color(green)(} \left(- 175\right)} = 0$

So the solutions are
color(white)("XXX")x=(-color(blue)(0)+-sqrt(color(blue)(0)-4 * (color(red)(1) * color(green)(""(-175)))))/(2 * color(red)(1))

$\textcolor{w h i t e}{\text{XXXX}} = \pm \frac{\sqrt{700}}{2}$

$\textcolor{w h i t e}{\text{XXXX}} = \pm \frac{10 \sqrt{7}}{2}$

$\textcolor{w h i t e}{\text{XXXX}} = \pm 5 \sqrt{7}$