Answer
$y=(x+2)^2-11$
Work Step by Step
\begin{align*}
&y=(x^2+4x)-7 &\text{Group the terms with variables together.}\\
\end{align*}
Recall:
To complete the square of $y=a(x^2+bx)+c$, you add $\left(\dfrac{b}{2}\right)^2$ inside the parentheses and subtract $a\cdot \left(\dfrac{b}{2}\right)^2$ outside to obtain $y=a\left[x^2+bx +\color{blue}{\left(\dfrac{b}{2}\right)^2}\right]+c-\color{red}{a\left(\dfrac{b}{2}\right)^2}$
\begin{align*}
&y=\left[x^2+4x+\color{blue}{\left(\frac{4}{2}\right)^2}\right]-7\color{red}{-\left(\frac{4}{2}\right)^2} &\text{Complete the square.}\\\\
&y=\left[x^2+4x+4\right]-7-4 &\text{Simplify.}\\\\
&y=(x+2)^2-11\\\\
\end{align*}
