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: 9


The solutions are $t=-4+3\sqrt{5}$ or $t=-4-3\sqrt{5}$

Work Step by Step

$ t^{2}+8t+16=45\qquad$ ...write left side as a binomial squared. ($16=4^{2}$) $(t+4)^{2}=45\qquad$ ...take square roots of each side. $ t+4=\pm\sqrt{45}\qquad$ ...add $-4$ to each side. $ t+4-4=\pm\sqrt{45}-4\qquad$ ...simplify. $ t=-4\pm\sqrt{45}\qquad$ ...rewrite $\sqrt{45}$ as $\sqrt{9\cdot 5.}$ $ t=-4\pm\sqrt{9\cdot 5}\qquad$ ...evaluate $\sqrt{9}$. $ t=-4\pm 3\sqrt{5}\qquad$ ...write as separate equations. $t=-4+3\sqrt{5}$ or $t=-4-3\sqrt{5}$
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