Answer
$=x^2+5x+\frac{25}{4}$
$=(x+\frac{5}{2})^2$
Work Step by Step
The given expression is
$=x^2+5x$
Find the value of $(\frac{b}{2})^2$.
Substitute $5$ for $b$.
$=(\frac{5}{2})^2$
Simplify.
$=\frac{25}{4}$
Add $\frac{25}{4}$ to the given expression.
$=x^2+5x+\frac{25}{4}$
Write the the polynomial as $a^2+2ab+b^2$.
$=x^2+2(x)(\frac{5}{2})+(\frac{5}{2})^2$
Use perfect square trinomial pattern
$a^2+2ab+b^2=(a+b)^2$
We have $a=x$ and $b=\frac{5}{2}$.
$=(x+\frac{5}{2})^2$
