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: 27


The solutions are $1+2i\sqrt{6}$ and $1-2i\sqrt{6}$.

Work Step by Step

$ x^{2}-2x+25=0\qquad$ ... write left side in the form $x^{2}+bx$ (add $-25$ to each side). $ x^{2}-2x+25-25=0-25\qquad$ ...simplify. $ x^{2}-2x=-25\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{-2}{2})^{2}=(-1)^{2}=1\qquad$ ...add $1$ to each side of the expression $ x^{2}-2x+1=-25+1\qquad$ ...simplify. $ x^{2}-2x+1=-24\qquad$ ... write left side as a binomial squared. $(x-1)^{2}=-24\qquad$ ...take square roots of each side. $ x-1=\pm\sqrt{-24}\qquad$ ...simplify.($\sqrt{-24}=i\sqrt{24}$) $ x-1=\pm i\sqrt{24}\qquad$ ...add $1$ to each side. $ x-1+1=\pm i\sqrt{24}+1\qquad$ ...simplify. $ x=1\pm i\sqrt{24}\qquad$ ...rewrite $\sqrt{24}$ as $\sqrt{4\cdot 6}$ $ x=1\pm i\sqrt{4\cdot 6.}\qquad$ ...evaluate $\sqrt{4}$. $x=1\pm 2i\sqrt{6}$
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