Answer
$\{-32,1\}$
Work Step by Step
Step 1. Let $u=(x)^{-1/5}$, we have $2u^2-u-1=0$
Step 2. Factor and solve: $(u-1)(2u+1)=0$ thus $u=-\frac{1}{2}, 1$
Step 3. For $u=-\frac{1}{2}$, we have $(x)^{-1/5}=-\frac{1}{2}$ thus $x=-32$
Step 4. For $u=1$, we have $(x)^{-1/5}=1$ thus $x=1$
Step 5. Solution set $\{-32,1\}$