# How do you solve x^2 +8x +16=0?

May 18, 2016

The solution is $x = - 4$

#### Explanation:

${x}^{2} + 8 x + 16 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 1 , b = 8 , c = 16$

The Discriminant is given by:

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

$= {\left(8\right)}^{2} - \left(4 \cdot 1 \cdot 16\right)$

$= 64 - 64 = 0$

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

$x = \frac{- 8 \pm \sqrt{0}}{2 \cdot 1} = \frac{- 8 \pm 0}{2}$

$x = \frac{- 8 + 0}{2} = - \frac{8}{2} = - 4$

$x = \frac{- 8 - 0}{2} = - \frac{8}{2} = - 4$