# How do you solve x^2 + 8x = 24 using the quadratic formula?

Sep 11, 2016

$x = - 4 \pm 2 \sqrt{10}$

#### Explanation:

We have: ${x}^{2} + 8 x = 24$

First, let's subtract $24$ from both sides of the equation:

$\implies {x}^{2} + 8 x - 24 = 0$

Then, let's apply the quadratic formula:

$\implies x = \frac{- 8 \pm \sqrt{{8}^{2} - 4 \left(1\right) \left(- 24\right)}}{2 \left(1\right)}$

$\implies x = \frac{- 8 \pm \sqrt{64 + 96}}{2}$

$\implies x = \frac{- 8 \pm \sqrt{160}}{2}$

$\implies x = \frac{- 8 \pm 4 \sqrt{10}}{2}$

$\implies x = - 4 \pm 2 \sqrt{10}$

Therefore, the solutions to the equation are $x = - 4 - 2 \sqrt{10}$ and $x = - 4 + 2 \sqrt{10}$.