Question

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

$q^2+\frac{3}{4}q$.

Short answer

The result is${\left(q+\frac{3}{8}\right)}^2$.

Step-by-step solution

Given Information.  

The Given expression is$q^2+\frac{3}{4}q$.

Identify b ,the coefficient of term having power one.  

$q^2+\frac{3}{4}q$

The coefficient of $q$is $\frac{3}{4}$.

So,$b=\frac{3}{4}$.

Find  12b2.

Substitute $b=\frac{3}{4}$.

$$\begin{gathered} ={\left(\frac{1}{2}\times \frac{3}{4}\right)}^2 \\ ={\left(\frac{3}{8}\right)}^2 \\ =\frac{9}{64} \end{gathered}$$

Add 964to binomial expression to complete the square.  

$q^2+\frac{3}{4}q+\frac{9}{64}$

Rewrite as a binomial square.

${\left(q+\frac{3}{8}\right)}^2$