Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - 4.7 Exercises - Skill Practice - Page 289: 52


The solutions are $-4$ and $-5$.

Work Step by Step

$ x^{2}+9x+20=0\qquad$ ...Write left side in the form $x^{2}+bx.$(add $-20$ to each side) $ x^{2}+9x=-20\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{9}{2})^{2}=\frac{81}{4}\qquad$ ...complete the square by adding$ \displaystyle \frac{81}{4}$ to each side of the expression $ x^{2}+9x+\displaystyle \frac{81}{4}=-20+\frac{81}{4}\qquad$ ...Write left side as a binomial squared. $(x+\displaystyle \frac{9}{2})^{2}=\frac{1}{4}\qquad$ ...take square roots of each side. $ x+\displaystyle \frac{9}{2}=\pm\sqrt{\frac{1}{4}}\qquad$ ...evaluate$\sqrt{\frac{1}{4}}$ $ x+\displaystyle \frac{9}{2}=\pm\frac{1}{2}\qquad$ ...add $-\displaystyle \frac{9}{2}$ to each side. $x=-\displaystyle \frac{9}{2}\pm\frac{1}{2}$
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