# How do you solve x^ { 2} + 12x = - 60?

May 8, 2017

#### Explanation:

First we need to add 60 to make the right-hand side 0:
${x}^{2} + 12 x + 60 = 0$
Since this quadratic equation is not factorable, we apply the quadratic equation:
$x = \frac{- 12 \pm \sqrt{{12}^{2} - 4 \cdot 1 \cdot 60}}{2 \cdot 1}$
$x = \frac{- 12 \pm \sqrt{- 96}}{2}$
Since we cannot square root a negative value, we use $i$ to denote $\sqrt{- 1}$ as the imaginary number
$x = - 6 \pm \frac{4 i \sqrt{6}}{2}$
$x = - 6 \pm 2 i \sqrt{6}$
Therefore, our answers are $x = - 6 + 2 i \sqrt{6}$ and $x = - 6 - 2 i \sqrt{6}$

May 8, 2017

$x = - 6 \pm i \sqrt{- 24}$

#### Explanation:

Give -

${x}^{2} + 12 x = - 60$

Let use completing the square method

${x}^{2} + 12 x + 36 = - 60 + 36$

${\left(x + 6\right)}^{2} = - 24$

$x + 6 = \pm i \sqrt{- 24}$

$x = - 6 \pm i \sqrt{- 24}$