Answer
$=x^2+7x+\frac{49}{4}$
$=(x+\frac{7}{2})^2$
Work Step by Step
The given expression is
$=x^2+7x$
Find the value of $(\frac{b}{2})^2$.
Substitute $7$ for $b$.
$=(\frac{7}{2})^2$
Simplify.
$=\frac{49}{4}$
Add $\frac{49}{4}$ to the given expression.
$=x^2+7x+\frac{49}{4}$
Write the the polynomial as $a^2+2ab+b^2$.
$=x^2+2(x)(\frac{7}{2})+(\frac{7}{2})^2$
Use perfect square trinomial pattern
$a^2+2ab+b^2=(a+b)^2$
We have $a=x$ and $b=\frac{7}{2}$.
$=(x+\frac{7}{2})^2$
$=x^2+7x+\frac{49}{4}$
$=(x+\frac{7}{2})^2$
