# How do you solve x^2−8x+16=0 using the quadratic formula?

Feb 22, 2017

$x = 4$

#### Explanation:

The quadratic formula is defined by:
$x = \frac{- b \left(\left(\frac{+}{-}\right) \sqrt{{b}^{2} - 4 a c}\right)}{2 a}$
where $a$ is the coefficient in front of ${x}^{2}$, $b$ is the coefficient in front of $x$, and c is the last coefficient.

Plugging in 1 for a, -8 for b, and 16 for c:

$x = \frac{8 \left(\left(\frac{+}{-}\right) \sqrt{64 - 4 \left(1\right) \left(16\right)}\right)}{2 \left(1\right)}$

Simplify:

$x = \frac{8 \left(\left(\frac{+}{-}\right) \sqrt{0}\right)}{2 \left(1\right)}$

$\sqrt{0} = 0$ and the positive and negative of 0 is just 0. So it becomes:

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