# How do you solve x^2 + 2x - 8 = 0?

May 21, 2016

#### Answer:

The solutions for the equation are:
color(blue)(x = 2

color(blue)(x = -4

#### Explanation:

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

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

The Discriminant is given by:

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

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

$= 4 + 32 = 36$

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

x = (-2)+-sqrt(36))/(2*1) = ((-2+-6))/2

$x = \frac{- 2 + 6}{2} = \frac{4}{2} = 2$ , color(blue)(x = 2

$x = \frac{- 2 - 6}{2} = - \frac{8}{2} = - 4$ , color(blue)(x = -4