(Moscow 2000, problem C2) Let $f(x)=x^{2}+12 x+30$. Solve the equation $f(f(f(f(f(x))))))=0$.
For $f(x)=(x+6)^{2}-6$, we have $f(x)+6=(x+6)^{2}$. Let $y=x+6$ and $g(y)=y^{2}$, then the equation becomes $g(g(g(g(g(y)))))=6$. This solves to $y= \pm 6^{1 / 32}$, so $x=-6 \pm 6^{1 / 32}$.

The following exercise has not been covered in class.