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: 26


The solutions are $9+ i\sqrt{5}$ and $9-i\sqrt{5}$.

Work Step by Step

$ x^{2}-18x+86=0\qquad$ ... write left side in the form $x^{2}+bx$ (add $-86$ to each side). $ x^{2}-18x+86-86=0+-86\qquad$ ...simplify. $ x^{2}-18x=-86\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{-18}{2})^{2}=9^{2}=81\qquad$ ...add $81$ to each side of the expression $ x^{2}-18x+81=-86+81\qquad$ ...simplify. $ x^{2}-18x+81=-5\qquad$ ... write left side as a binomial squared. $(x-9)^{2}=-5\qquad$ ...take square roots of each side. $ x-9=\pm\sqrt{-5}\qquad$ ...simplify.($\sqrt{-5}=i\sqrt{5}$) $ x-9=\pm i\sqrt{5}\qquad$ ...add $9$ to each side. $ x-9+9=\pm i\sqrt{5}+9\qquad$ ...simplify. $x=9\pm i\sqrt{5}$
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