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 - Guided Practice for Examples 3, 4, and 5 - Page 286: 8


The solutions are $5+\sqrt{17}$ and $5-\sqrt{17}$.

Work Step by Step

$ x^{2}-10x+8=0\qquad$ ... write left side in the form $x^{2}+bx$ (add $-8$ to each side). $ x^{2}-10x=-8\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{-10}{2})^{2}=5^{2}=25\qquad$ ...add $25$ to each side of the expression $ x^{2}-10x+25=-8+25\qquad$ ... write left side as a binomial squared. $(x-5)^{2}=-8+25\qquad$ ...simplify. $(x-5)^{2}=17\qquad$ ...take square roots of each side. $ x-5=\pm\sqrt{17}\qquad$ ...add $5$ to each side $ x-5+5=\pm\sqrt{17}+5\qquad$ ...simplify. $x=5\pm\sqrt{17}$
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