Complete the square in the form $(px+q)^2+r, p > 0$ I'm going over some completing the square questions and I need to express, in the form:
$(px+q)^2+r, p &gt; 0$

the quadratic equation is $16x^2-8x+11$

I know how to get it in the form $p(x+q)^2+r$

So can someone show me how to get from $ax^2+bx+c$ to $(px+q)^2+r, p &gt; 0$
You can either do:

$$(px + q)^2 + r = 16x^2 - 8x + 11 \iff p^2x^2 + 2pqx + q^2 + r = 16x^2 - 8x + 11$$ and find the values of $p,q,r$ by identification, or do:

$$16x^2 - 8x + 11 = (4x)^2 - 2(4x)(1) + 11 = (4x)^2 - 2(4x)(1) + 1^2 + 10 = (4x - 1)^2 + 10$$

Hence:

$$p = 4, \ q = -1,\ r = 10$$
\begin{align*}16x^2 - 8x + 11 &amp;= 16 \left(x^2 - \frac12\right) +11\\
               &amp;= 16\left[\left( x- \frac12\right)^2 -\frac14\right] + 11\\
               &amp;= 16\left( x- \frac12\right)^2 - 4 + 11\\
               &amp;= \left[\sqrt{16} \left(x-\frac12\right)\right]^2 + 7\\
               &amp;= \left(4x - 2\right)^2 + 7
\end{align*}