# How do you solve 8m^2 - 2m = 7 using the quadratic formula?

Jun 3, 2018

See a solution process below:

#### Explanation:

First, put the equation in standard form:

$8 {m}^{2} - 2 m - \textcolor{red}{7} = 7 - \textcolor{red}{7}$

$8 {m}^{2} - 2 m - 7 = 0$

We can now use the quadratic equation to solve this problem:

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:

$\textcolor{red}{8}$ for $\textcolor{red}{a}$

$\textcolor{b l u e}{- 2}$ for $\textcolor{b l u e}{b}$

$\textcolor{g r e e n}{- 7}$ for $\textcolor{g r e e n}{c}$ gives:

$x = \frac{- \textcolor{b l u e}{- 2} \pm \sqrt{{\textcolor{b l u e}{- 2}}^{2} - \left(4 \cdot \textcolor{red}{8} \cdot \textcolor{g r e e n}{- 7}\right)}}{2 \cdot \textcolor{red}{8}}$

$m = \frac{2 \pm \sqrt{4 - \left(32 \cdot \textcolor{g r e e n}{- 7}\right)}}{16}$

$m = \frac{2 \pm \sqrt{4 - \left(- 224\right)}}{16}$

$m = \frac{2 \pm \sqrt{4 + 224}}{16}$

$m = \frac{2 \pm \sqrt{228}}{16}$

$m = \frac{2 \pm \sqrt{4 \cdot 57}}{16}$

$m = \frac{2 \pm \sqrt{4} \sqrt{57}}{16}$

$m = \frac{2 \pm 2 \sqrt{57}}{16}$

$m = \frac{2}{16} \pm \frac{2 \sqrt{57}}{16}$

$m = \frac{1}{8} \pm \frac{\sqrt{57}}{8}$

$m = \frac{1 \pm \sqrt{57}}{8}$

The Solution Set Is:

$m = \left\{\begin{matrix}\frac{1 - \sqrt{57}}{8} \\ \frac{1 + \sqrt{57}}{8}\end{matrix}\right\}$