# What is the solution set for  x^2 + 6x + 10 = 0?

Aug 10, 2015

$x = \frac{- 6 + \sqrt{- 4}}{2}$
$x = \frac{- 6 - \sqrt{- 4}}{2}$

#### Explanation:

Since ------- ${6}^{2}$ - $\left(4 \times 1 \times 10\right)$ < 0, x has imaginary roots

$x = \frac{- b \pm \sqrt{{b}^{2} - \left(4 a c\right)}}{2 a}$
$x = \frac{- 6 \pm \sqrt{{6}^{2} - \left(4 \times 1 \times 10\right)}}{2 \times 1}$
$x = \frac{- 6 \pm \sqrt{36 - 40}}{2}$
$x = \frac{- 6 + \sqrt{- 4}}{2}$
$x = \frac{- 6 - \sqrt{- 4}}{2}$