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: 22


The solutions are $-2+\sqrt{14}$ and $-2-\sqrt{14}$.

Work Step by Step

$ x^{2}+4x=10\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{4}{2})^{2}=2^{2}=4\qquad$ ...add $4$ to each side of the expression $ x^{2}+4x+4=10+4\qquad$ ... write left side as a binomial squared. $(x+2)^{2}=10+4\qquad$ ...simplify. $(x+2)^{2}=14\qquad$ ...take square roots of each side. $ x+2=\pm\sqrt{14}\qquad$ ...add $-2$ to each side $ x+2-2=\pm\sqrt{14}-2\qquad$ ...simplify. $x=-2\pm\sqrt{14}$
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