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: 11


The solutions are $x=\displaystyle \frac{2+i\sqrt{3}}{3}$ or $x=\displaystyle \frac{2-i\sqrt{3}}{3}$.

Work Step by Step

$ 9x^{2}-12x+4=-3\qquad$ ...write left side as a binomial squared.($(a\pm b)^{2}=a^{2}\pm 2ab+b^{2}$) $a=3x,b=2$ $(3x-2)^{2}=-3\qquad$ ...take square roots of each side. $ 3x-2=\pm\sqrt{-3}\qquad$ ...add $2$ to each side. $ 3x-2+2=\pm\sqrt{-3}+2\qquad$ ...simplify.($\sqrt{-3}=i\sqrt{3}$). $ 3x=2\pm i\sqrt{3}\qquad$ ...divide both sides wirh $2$. $ x=\displaystyle \frac{2\pm i\sqrt{3}}{3}\qquad$ ...write as separate equations. $x=\displaystyle \frac{2+i\sqrt{3}}{3}$ or $x=\displaystyle \frac{2-i\sqrt{3}}{3}$
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