# How do you solve –4 sqrt(x+2) + 3 = -9?

Jun 20, 2016

$x = 7$

#### Explanation:

First, isolate the term including $x$ using subtraction.

$- 4 \sqrt{x + 2} + 3 = - 9$

$\implies - 4 \sqrt{x + 2} + 3 - 3 = - 9 - 3$

$\implies - 4 \sqrt{x + 2} = - 12$

Next, change the coefficient of $\sqrt{x + 2}$ to $1$ using division.

$\implies \frac{- 4 \sqrt{x + 2}}{- 4} = \frac{- 12}{- 4}$

$\implies \sqrt{x + 2} = 3$

Next, eliminate the square root by squaring each side.

$\implies {\left(\sqrt{x + 2}\right)}^{2} = {3}^{2}$

$\implies x + 2 = 9$

Finally, isolate $x$ using subtraction.

$\implies x + 2 - 2 = 9 - 2$

$\implies x = 7$

$- 4 \sqrt{7 + 2} + 3 = - 4 \sqrt{9} + 3$
$= - 4 \left(3\right) + 3$
$= - 12 + 3$
$= - 9$