# How do you solve (x+7)^(3/2)-20=7?

Apr 22, 2018

$x = 2$

#### Explanation:

${\left(x + 7\right)}^{\frac{3}{2}} - 20 = 7$

Rearrange equation.

${\left(x + 7\right)}^{\frac{3}{2}} = 27$

To get rid of the power, first cube root it and then square it.

$\left({\left(x + 7\right)}^{\frac{3}{2} \cdot \frac{1}{3}}\right) = {27}^{\frac{1}{3}}$

${\left(x + 7\right)}^{\frac{3}{6}} = 3 \to {\left(x + 7\right)}^{\frac{1}{2}} = 3$

${\left(x + 7\right)}^{\frac{1}{2} \cdot 2} = {3}^{2} \to x + 7 = 9$

Rearrange equation to make $x$ the subject.

$x + 7 = 9 \to x = 9 - 7$
$x = 2$