# How do you use the quadratic formula to solve x^2+4x-2=0?

Jun 12, 2018

See a solution process below:

#### Explanation:

For $\textcolor{red}{a} {x}^{2} + \textcolor{b l u e}{b} x + \textcolor{g r e e n}{c} = 0$, the values of $x$ which are the solutions to the equation are given by:

$x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - \left(4 \textcolor{red}{a} \textcolor{g r e e n}{c}\right)}}{2 \cdot \textcolor{red}{a}}$

Substituting:

$\textcolor{red}{1}$ for $\textcolor{red}{a}$

$\textcolor{b l u e}{4}$ for $\textcolor{b l u e}{b}$

$\textcolor{g r e e n}{- 2}$ for $\textcolor{g r e e n}{c}$ gives:

$x = \frac{- \textcolor{b l u e}{4} \pm \sqrt{{\textcolor{b l u e}{4}}^{2} - \left(4 \cdot \textcolor{red}{1} \cdot \textcolor{g r e e n}{- 2}\right)}}{2 \cdot \textcolor{red}{1}}$

$x = \frac{- \textcolor{b l u e}{4} \pm \sqrt{16 - \left(- 8\right)}}{2}$

$x = \frac{- \textcolor{b l u e}{4} \pm \sqrt{24}}{2}$

$x = \frac{- \textcolor{b l u e}{4} \pm \sqrt{4 \cdot 6}}{2}$

$x = \frac{- \textcolor{b l u e}{4} \pm \left(\sqrt{4} \sqrt{6}\right)}{2}$

$x = \frac{- \textcolor{b l u e}{4} \pm 2 \sqrt{6}}{2}$

$x = - \frac{\textcolor{b l u e}{4}}{2} \pm \frac{2 \sqrt{6}}{2}$

$x = - 2 \pm \sqrt{6}$

$x = \left\{\begin{matrix}- 2 - \sqrt{6} \\ - 2 + \sqrt{6}\end{matrix}\right\}$