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 288: 23


The solutions are $-4+\sqrt{15}$ and $-4-\sqrt{15}$.

Work Step by Step

$ x^{2}+8x=-1\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{8}{2})^{2}=4^{2}=16\qquad$ ...add $16$ to each side of the expression $ x^{2}+8x+16=-1+16\qquad$ ... write left side as a binomial squared. $(x+4)^{2}=-1+16\qquad$ ...simplify. $(x+4)^{2}=15\qquad$ ...take square roots of each side. $ x+4=\pm\sqrt{15}\qquad$ ...add $-4$ to each side $ x+4-4=\pm\sqrt{15}-4\qquad$ ...simplify. $x=-4\pm\sqrt{15}$
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