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: 30


The solutions are $x=5+2\sqrt{7}$ and $x=5-2\sqrt{7}$.

Work Step by Step

$ 4x^{2}-40x-12=0\qquad$ ...divide each term with $4$. $ x^{2}-10x-3=0\qquad$ ...add $3$ to each side. $ x^{2}-10x-3+3=0+3\qquad$ ...simplify. $ x^{2}-10x=3\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=3+25\qquad$ ...simplify. $ x^{2}-10x+25=28\qquad$ ... write left side as a binomial squared. $(x-5)^{2}=28\qquad$ ...take square roots of each side. $ x-5=\pm\sqrt{28}\qquad$ ...rewrite $\sqrt{28}$ as $\sqrt{4\cdot 7}$ $ x-5=\pm\sqrt{4\cdot 7}\qquad$ ...evaluate $\sqrt{4}$. $ x-5=\pm 2\sqrt{7}\qquad$ ...add $5$ to each side. $x=5\pm 2\sqrt{7}$
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