Question

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

$y^2+11y$.

Short answer

The result is${\left(y+\frac{11}{2}\right)}^2$.

Step-by-step solution

Given Information. 

The Given expression is $y^2+11y$.

Identify b ,the coefficient of term having power one. 

$y^2+11y$

The coefficient of $y$is $11$.

So,$b=11$.

Find 12b2.

Substitute $b=11$.

$$\begin{gathered} ={\left(\frac{1}{2}\times 11\right)}^2 \\ ={\left(\frac{11}{2}\right)}^2 \\ =\frac{121}{4} \end{gathered}$$

Add 1214to binomial expression to complete the square. 

$y^2+11y+\frac{121}{4}$

Rewrite as a binomial square.

${\left(y+\frac{11}{2}\right)}^2$.