Answer
$\{-8,2\}$
Work Step by Step
Step 1. Given the equation $\sqrt[4] {x^2+6x}=2$
Step 2. Raise to the 4th power on both sides to get: $x^2+6x=16$ or $x^2+6x-16=0$ which gives $x=-8,2$
Step 3. Check answer in the original equation: both $\{-8,2\}$ fit.
