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: 31


The solutions are $s=-1+i\sqrt{2}$ and $s=-1-i\sqrt{2}$.

Work Step by Step

$ 3s^{2}+6s+9=0\qquad$ ...divide each term with $3$. $ s^{2}+2s+3=0\qquad$ ...add $-3$ to each side. $ s^{2}+2s+3-3=0-3\qquad$ ...simplify. $ s^{2}+2s=-3\qquad$ ...square half the coefficient of $s$. $(\displaystyle \frac{2}{2})^{2}=(1)^{2}=1\qquad$ ...add $1$ to each side of the expression $ s^{2}+2s+1=-3+1\qquad$ ...simplify. $ s^{2}+2s+1=-2\qquad$ ... write left side as a binomial squared. $(s+1)^{2}=-2\qquad$ ...take square roots of each side. $ s+1=\pm\sqrt{-2}\qquad$ ...simplify.($\sqrt{-2}=i\sqrt{2}$) $ s+1=\pm i\sqrt{2}\qquad$ ...add $-1$ to each side. $ s+1-1=\pm i\sqrt{2}-1\qquad$ ...simplify. $s=-1\pm i\sqrt{2}$
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