# How do you solve x^2+8=0 using the quadratic formula?

Jan 16, 2017

$x = 2 \sqrt{2} \textcolor{w h i t e}{\text{x")icolor(white)("XXX")orcolor(white)("XXX")x=-2sqrt(2)color(white)("x}} i$

(see below for use of the quadratic formula)

#### Explanation:

Standard quadratic form for an equation is:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{a} {x}^{2} + \textcolor{b l u e}{b} x + \textcolor{m a \ge n t a}{c} = 0$
and in this form the solutions are given by
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - 4 \textcolor{red}{a} \textcolor{m a \ge n t a}{c}}}{2 \textcolor{red}{a}}$

Expressing the given equation into standard form:
${x}^{2} + 8 = 0$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow \textcolor{red}{1} {x}^{2} + \textcolor{b l u e}{0} \cdot x + \textcolor{m a \ge n t a}{8} = 0$
with solutions:
$\textcolor{w h i t e}{\text{XXX}} x = \frac{- \textcolor{b l u e}{0} \pm \sqrt{{\textcolor{b l u e}{0}}^{2} - 4 \cdot \textcolor{red}{1} \cdot \textcolor{m a \ge n t a}{8}}}{2 \cdot \textcolor{red}{1}}$

$\textcolor{w h i t e}{\text{XXX")=+-sqrt(-32)/2=+-(4sqrt(2)color(white)("x")i)/2=+-2sqrt(2)color(white)("x}} i$