# How do you solve x² - 4x - 8 = 4?

Apr 9, 2016

$x = 6 , - 2$

#### Explanation:

color(blue)(x^2-4x-8=4

Subtract $4$ both sides

$\rightarrow {x}^{2} - 4 x - 8 - 4 = 4 - 4$

$\rightarrow {x}^{2} - 4 x - 12 = 0$

This is a Quadratic equation (in form $a {x}^{2} + b x + c = 0$)

color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)

Remember that, $a \mathmr{and} b$ are the coefficients and $c$ is the constant term

So,

color(orange)(a=1,b=-4,c=-12

$\rightarrow x = \frac{- \left(- 4\right) \pm \sqrt{- {4}^{2} - 4 \left(1\right) \left(- 12\right)}}{2 \left(1\right)}$

$\rightarrow x = \frac{4 \pm \sqrt{16 - \left(- 48\right)}}{2}$

$\rightarrow x = \frac{4 \pm \sqrt{16 + 48}}{2}$

$\rightarrow x = \frac{4 \pm \sqrt{64}}{2}$

$\rightarrow x = \frac{4 \pm 8}{2}$

Now we have two solutions

color(purple)(x=(4+8)/(2)=12/2=6

color(violet)(x=(4-8)/(2)=-4/2=-2