Completing the square is a technique for converting a quadratic polynomial of the form

\begin{equation*}
ax^2+bx+c
\end{equation*}

to

\begin{equation*}
a(x-h)^2+k
\end{equation*}

where 

\begin{equation*}
h = - \frac{b}{2a}
\end{equation*}

\begin{equation*}
k = c - ah^2 = c - \frac{b^2}{4a}
\end{equation*}
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