Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 787: 3



Work Step by Step

$x-2\sqrt{x}=8$ Take the $8$ to the left side of the equation and the $2\sqrt{x}$ to the right side: $x-8=2\sqrt{x}$ Square both sides of the equation: $(x-8)^{2}=(2\sqrt{x})^{2}$ $x^{2}-16x+64=4x$ Take the $4x$ to the left side of the equation and simplify it by combining like terms: $x^{2}-16x-4x+64=0$ $x^{2}-20x+64=0$ Solve this equation by factoring: $(x-16)(x-4)=0$ Make both factor equal to $0$ and solve each individual equation: $x-16=0$ $x=16$ $x-4=0$ $x=4$ Check the answers by substituting them into the original equation: $x=16$ $16-2\sqrt{16}=8$ $8=8$ True $x=4$ $4-2\sqrt{4}=8$ $0\ne8$ False The final solution is $x=16$
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