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: 29


The solutions are $x=-7+\sqrt{41}$ and $x=-7-\sqrt{41}$.

Work Step by Step

$ 3x^{2}+42x=-24\qquad$ ...divide each side with $3$. $ x^{2}+14x=-8\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{14}{2})^{2}=(7)^{2}=49\qquad$ ...add $49$ to each side of the expression $ x^{2}+14x+49=-8+49\qquad$ ...simplify. $ x^{2}+14x+49=41\qquad$ ... write left side as a binomial squared. $(x+7)^{2}=41\qquad$ ...take square roots of each side. $ x+7=\pm\sqrt{41}\qquad$ ...add $-7$ to each side. $ x+7-7=\pm\sqrt{41}-7\qquad$ ...simplify. $x=-7\pm\sqrt{41}$
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