# How do you solve x^2 − 8x − 4 = 0 using the quadratic formula?

Aug 10, 2015

The solutions for the equation are:
color(blue)(x=4+2sqrt5
 color(blue)(x=4-2sqrt5

#### Explanation:

 x^2−8x−4=0

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

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$

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

$= 64 + 16$

$= 80$

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

$x = \frac{- \left(- 8\right) \pm \sqrt{80}}{2 \cdot 1} = \frac{8 \pm 4 \sqrt{5}}{2}$

$x = \frac{\cancel{2} \left(4 \pm 2 \sqrt{5}\right)}{\cancel{2}}$

$x = 4 \pm 2 \sqrt{5}$

The solutions are
color(blue)(x=4+2sqrt5 , color(blue)(x=4-2sqrt5