# How do you solve 2(x + 8) ^ (4/5) - 12 = 150 and find any extraneous solutions?

Jul 30, 2016

$x = 235$

#### Explanation:

$2 {\left(x + 8\right)}^{\frac{4}{5}} - 12 = 150$
or
$2 {\left(x + 8\right)}^{\frac{4}{5}} = 150 + 12$
or
$2 {\left(x + 8\right)}^{\frac{4}{5}} = 162$
or
${\left(x + 8\right)}^{\frac{4}{5}} = \frac{162}{2}$
or
${\left(x + 8\right)}^{\frac{4}{5}} = 81$
or
$\left(x + 8\right) = {81}^{\frac{5}{4}}$
or
$x + 8 = {\left(\sqrt[4]{81}\right)}^{5}$
or
$x + 8 = {\left(\sqrt[4]{\left(3\right) \left(3\right) \left(3\right) \left(3\right)}\right)}^{5}$
or
$x + 8 = {3}^{5}$
or
$x + 8 = 243$
or
$x = 243 - 8$
or
$x = 235$