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: 35



Work Step by Step

Length $\times$ Width $=$ Area of a rectangle. $ x(x+10)=50\qquad$ ...Distributive property $ x^{2}+10x=50\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=50+25\qquad$ ...simplify. $ x^{2}+10x+25=75\qquad$ ...write left side as a binomial squared. $(x+5)^{2}=75\qquad$ ...take square roots of each side. $ x+5=\pm\sqrt{75}\qquad$ ...rewrite $\sqrt{75}$ as $\sqrt{25\cdot 3}$ $ x+5=\pm\sqrt{25\cdot 3}\qquad$ ...evaluate $\sqrt{25}$. $ x+5=\pm 5\sqrt{3}\qquad$ ...add $-5$ to each side. $ x+5-5=\pm 5\sqrt{3}-5\qquad$ ...simplify. $x=-5\pm 5\sqrt{3}$ $x=-5+5\sqrt{3}$ or $x=-5-5\sqrt{3}$. We are calculating length, which cannot be negative. The solution $x=-5-5\sqrt{3}$ is negative, so we discard it. Solution: $x=-5+5\sqrt{3}$
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