# Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - 4.7 Exercises - Skill Practice - Page 288: 19

The trinomial $x^{2}+7x+c$ is a perfect square when $c=\displaystyle \frac{49}{4}.$ Then $x^{2}+7x+\displaystyle \frac{49}{4}=(x+\frac{7}{2})(x+\frac{7}{2})=(x+\frac{7}{2})^{2}$

#### Work Step by Step

$x^{2}+7x+c\qquad$ ... find half the coefficient of $x$, which is $\displaystyle \frac{7}{2}$. $\qquad$ ...square the result. $(\displaystyle \frac{7}{2})^{2}=\frac{49}{4}\qquad$ ...substitute $c$ with $\displaystyle \frac{49}{4}$ in the original expression $x^{2}+7x+\displaystyle \frac{49}{4}=(x+\frac{7}{2})^{2}$

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