# How do you solve x^2 = 8x - 20 using the quadratic formula?

Mar 4, 2016

The solutions are:
color(blue)(x=4+ 2i

color(blue)(x=4- 2i

#### Explanation:

${x}^{2} - 8 x + 20 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = - 8 , c = 20$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$
$= {\left(- 8\right)}^{2} - \left(4 \cdot 1 \cdot 20\right)$
$= 64 - 80 = - 16$

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

$x = \frac{- \left(- 8\right) \pm \sqrt{- 16}}{2 \cdot 1} = \frac{8 \pm 4 i}{2}$

$x = \frac{2 \left(4 \pm 2 i\right)}{2}$

$x = \frac{\cancel{2} \left(4 \pm 2 i\right)}{\cancel{2}}$

color(blue)(x=4+ 2i

color(blue)(x=4- 2i