Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - Guided Practice for Examples 1 and 2 - Page 285: 6

$c=\displaystyle \frac{81}{4}$ $(x-\displaystyle \frac{9}{2})^{2}$

Work Step by Step

$x^{2}-9x+c\qquad$ ... find half the coefficient of $x$, which is $\displaystyle \frac{-9}{2}$. $\qquad$ ...square the result. $(\displaystyle \frac{-9}{2})^{2}=\frac{81}{4}\qquad$ ...substitute $c$ with $\displaystyle \frac{81}{4}$ in the original expression $x^{2}-9x+\displaystyle \frac{81}{4}=(x-\frac{9}{2})^{2}$ The trinomial $x^{2}-9x+c$ is a perfect square when $c=\displaystyle \frac{81}{4}.$ Then $x^{2}-9x+\displaystyle \frac{81}{4}=(x-\frac{9}{2})(x-\frac{9}{2})=(x-\frac{9}{2})^{2}$.

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