# How do you solve for x in 3(x-6)^(5/2) = 96?

Apr 24, 2015

$3 {\left(x - 6\right)}^{\frac{5}{2}} = 96$

Reduce by removing obvious common factor ($3$)
$\rightarrow {\left(x - 6\right)}^{\frac{5}{2}} = 32$

Note that $32 = {2}^{5}$ so we can take the 5th root of both sides
$\rightarrow {\left(x - 6\right)}^{\frac{1}{2}} = 2$

Square both sides to clear the root on the left side
$\rightarrow x - 6 = 4$

Isolate $x$
$\rightarrow x = 10$