# How do you solve x^2 – 4x – 8 = 0?

Apr 17, 2016

color(green)(x= 2 + sqrt3

$\textcolor{g r e e n}{x = 2 - \sqrt{3}}$

#### Explanation:

${x}^{2} - 4 x - 8 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = - 4 , c = - 8$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(- 4\right)}^{2} - \left(4 \cdot 1 \cdot - \left(8\right)\right)$

$= 16 + 32 = 48$

The solutions are found using the formula:
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{- \left(- 4\right) \pm \sqrt{48}}{2 \cdot 1} = \frac{4 \pm \sqrt{48}}{2}$

$\sqrt{48} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 3} = \sqrt{{2}^{2} \cdot {2}^{2} \cdot 3} = 4 \sqrt{3}$

$x = \frac{4 \pm \sqrt{48}}{2} = \frac{4 \pm 4 \sqrt{3}}{2}$

$= \frac{\left(\cancel{4}\right) \cdot \left(1 \pm \sqrt{3}\right)}{\cancel{2}}$

$x = \left(2\right) \cdot \left(1 + \sqrt{3}\right)$
color(green)(x= 2 + sqrt3

x= (2) * ( 1 - sqrt3))
$\textcolor{g r e e n}{x = 2 - \sqrt{3}}$