# Question #20bba

Nov 8, 2016

$x = - \frac{1}{2}$ and $x = - \frac{3}{2}$

#### Explanation:

Solve using the quadratic formula: $4 {x}^{2} + 8 x = - 3$

To use the quadratic formula, the equation must be in the form
$a {x}^{2} + b x + c = 0$

Add 3 to both sides to get all the terms on the left.

$4 {x}^{2} + 8 x \textcolor{w h i t e}{a a a} = - 3$
$\textcolor{w h i t e}{a a a a a a a} + 3 \textcolor{w h i t e}{a a a} + 3$

$\textcolor{red}{4} {x}^{2} + \textcolor{b l u e}{8} x + \textcolor{m a \ge n t a}{3} = 0$

$\textcolor{red}{a} = \textcolor{red}{4} , \textcolor{b l u e}{b} = \textcolor{b l u e}{8} , \textcolor{m a \ge n t a}{c} = \textcolor{m a \ge n t a}{3}$

$x = \frac{- \textcolor{b l u e}{b} \pm \sqrt{{\textcolor{b l u e}{b}}^{2} - 4 \textcolor{red}{a} \textcolor{m a \ge n t a}{c}}}{2 \textcolor{red}{a}}$

$x = \frac{- \textcolor{b l u e}{8} \pm \sqrt{{\textcolor{b l u e}{8}}^{2} - 4 \left(\textcolor{red}{4}\right) \left(\textcolor{m a \ge n t a}{3}\right)}}{2 \left(\textcolor{red}{4}\right)}$

$x = \frac{- 8 \pm \sqrt{64 - 48}}{8}$

$x = \frac{- 8 \pm \sqrt{16}}{8}$

$x = \frac{- 8 \pm 4}{8}$

Separate into two equations, one with a plus in the numerator and the other with a minus.

$x = \frac{- 8 + 4}{8} \textcolor{w h i t e}{a a a a} x = \frac{- 8 - 4}{8}$

$x = \frac{- 4}{8} \textcolor{w h i t e}{a a a a a a a} x = \frac{- 12}{8}$

$x = - \frac{1}{2} \textcolor{w h i t e}{a a a a a a a a} x = - \frac{3}{2}$