# How do you solve the quadratic using the quadratic formula given -c^2-6c+8=0 over the set of complex numbers?

Jan 2, 2018

$c = \frac{- 6 \pm 2 \sqrt{17}}{2}$

#### Explanation:

The quadratic formula states that if you have an equation in the form:
$n {x}^{2} + p x + q = 0$

The solution(s) will be:
$x = \frac{- p \pm \sqrt{{p}^{2} - 4 n q}}{2 n}$

In our case $n = - 1 , p = - 6$ and $q = 8$, and applying the quadratic formula gives us:
$c = \frac{- \left(- 6\right) \pm \sqrt{{\left(- 6\right)}^{2} - 4 \cdot - 1 \cdot 8}}{2 \cdot - 1}$

$c = \frac{6 \pm \sqrt{36 - \left(- 32\right)}}{-} 2$

$c = - \frac{6 \pm \sqrt{36 + 32}}{2}$

$c = \frac{- 6 \pm \sqrt{68}}{2}$

$c = \frac{- 6 \pm \sqrt{2 \cdot 2 \cdot 17}}{2}$

$c = \frac{- 6 \pm 2 \sqrt{17}}{2}$