# How do you solve -x^2-12=-87?

Mar 7, 2018

$x = \pm 5 \sqrt{3}$

#### Explanation:

If
$\textcolor{w h i t e}{\text{XXX}} - {x}^{2} - 12 = - 87$
then
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} + 12 = 87$

$\textcolor{w h i t e}{\text{XXX}} {x}^{2} = 75$

$\textcolor{w h i t e}{\text{XXX}} x = \pm 5 \sqrt{3}$

Mar 7, 2018

$x = \pm 5 \sqrt{3}$

#### Explanation:

Multiply all of both sides by (-1)

$+ {x}^{2} + 12 = + 87$

Subtract 12 from both sides

${x}^{2} = 87 - 12 = 75$

$x = \sqrt{75}$

But 75 $\to 5 \times 15 \to 5 \times 5 \times 3 = {5}^{2} \times 3$

$x = \sqrt{{5}^{2} \times 3}$

$x = 5 \sqrt{3}$ as an EXACT principle root answer (only positive)

However. This is a quadratic so it will have both positive and negative roots. The plot will cross the x-axis in 2 places

$x = \pm 5 \sqrt{3}$