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: 7


The solutions are $x=11+\sqrt{13}$ or $x=11-\sqrt{13}$.

Work Step by Step

$ x^{2}-22x+121=13\qquad$ ...write left side as a binomial squared. ($121=11^{2}$) $(x-11)^{2}=13\qquad$ ...take square roots of each side. $ x-11=\pm\sqrt{13}\qquad$ ...add $11$ to each side. $ x-11+11=\pm\sqrt{13}+11\qquad$ ...simplify. $ x=11\pm\sqrt{13}\qquad$ ...write as separate equations. $x=11+\sqrt{13}$ or $x=11-\sqrt{13}$
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