# How do you solve x^2 - 4x - 32 = 0?

Mar 23, 2018

The root of the equation is $x = 2 \pm 6$ or $x = 8$ and $x = - 4$.

#### Explanation:

For an equation in the form of $a {x}^{2} + b x + c = 0$, the quadratic formula ($x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$) can be applied.

Plugging in $1$ for $a$, $- 4$ for $b$, and $- 32$ for $c$:

$x = \frac{- \left(- 4\right) \pm \sqrt{{\left(- 4\right)}^{2} - 4 \left(1\right) \left(- 32\right)}}{2 \left(1\right)}$

$x = \frac{4 \pm \sqrt{16 - 4 \left(- 32\right)}}{2}$

$x = \frac{4 \pm \sqrt{16 - \left(- 128\right)}}{2}$

$x = \frac{4 \pm \sqrt{144}}{2}$

$x = \frac{4}{2} \pm \frac{\sqrt{144}}{2}$

$x = 2 \pm \frac{12}{2}$

$x = 2 \pm 6$

$x = 2 + 6 = 8$
$x = 2 - 6 = - 4$