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: 32


The solutions are $t=-2+2i$ and $t=-2-2i$.

Work Step by Step

$ 7t^{2}+28t+56=0\qquad$ ...divide each term with $7$. $ t^{2}+4t+8=0\qquad$ ...add $-8$ to each side. $ t^{2}+4t+8-8=0-8\qquad$ ...simplify. $ t^{2}+4t=-8\qquad$ ...square half the coefficient of $t$. $(\displaystyle \frac{4}{2})^{2}=(2)^{2}=4\qquad$ ...add $4$ to each side of the expression $ t^{2}+4t+4=-8+4\qquad$ ...simplify. $ t^{2}+4t+4=-4\qquad$ ... write left side as a binomial squared. $(t+2)^{2}=-4\qquad$ ...take square roots of each side. $ t+2=\pm\sqrt{-4}\qquad$ ...simplify.($\sqrt{-4}=2i$) $ t+2=\pm 2i\qquad$ ...add $-2$ to each side. $ t+2-2=\pm 2i-2\qquad$ ...simplify. $t=-2\pm 2i$
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