Answer
$[-8,0]$ or $\{x|-8\le x\le0\}$.
Work Step by Step
Step 1. $x^2+8x\le0 \longrightarrow x(x+8)\le0$.
Step 2. Identify boundary points $x=-8,0$ and form intervals $(-\infty-8],[-8,0],[0,\infty)$.
Step 3. Choose test values $x=-9,-1,1$ to test the inequality and get results $False,\ True,\ False$.
Step 4. Thus we have the solution $[-8,0]$ or $\{x|-8\le x\le0\}$.
