Answer
$f(x)=(x+4)^2-5$
Work Step by Step
Given the function $$f(x)=x^2+8x+11.$$ To complete the square of the function, we add and subtract half the square of the middle term and simplify: \begin{equation}
\begin{aligned}
f(x) & =x^2+8 x+11 \\
& =x^2+2\cdot 4x+4^2-4^2+11 \\
& =(x+4)^2-5.
\end{aligned}
\end{equation} Hence the function can be written as $$f(x)=(x+4)^2-5.$$
