# How do you factor n^2+5n+7?

Oct 1, 2015

$n = \left(\frac{- 5 + \sqrt{3} i}{2}\right) , \left(\frac{- 5 - \sqrt{3} i}{2}\right)$

#### Explanation:

${n}^{2} + 5 n + 7$ is a quadratic equation $a {x}^{2} + b x + c$, where $a = 1 , b = 5 , c = 7$.

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Substitute $n$ for $x$.

$n = \frac{- 5 \pm \sqrt{{5}^{2} - 4 \cdot 1 \cdot 7}}{2 \cdot 1} =$

Simplify.

$n = \frac{- 5 \pm \sqrt{25 - 28}}{2} =$

Simplify.

$n = \frac{- 5 \pm \sqrt{- 3}}{2} =$

Simplify.

$n = \frac{- 5 \pm \sqrt{3} i}{2} =$

$n = \left(\frac{- 5 + \sqrt{3} i}{2}\right) , \left(\frac{- 5 - \sqrt{3} i}{2}\right)$