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: 4

Answer

$x=8$

Work Step by Step

$x-\sqrt{2x}=4$ Take the $4$ to the left side of the equation and $\sqrt{2x}$ to the right side: $x-4=\sqrt{2x}$ Square both sides of the equation: $(x-4)^{2}=(\sqrt{2x})^{2}$ $x^{2}-8x+16=2x$ Take the $2x$ to the left side of the equation and simplify it by combining like terms: $x^{2}-8x-2x+16=0$ $x^{2}-10x+16=0$ Solve this equation by factoring: $(x-8)(x-2)=0$ Set both factors equal to $0$ and solve each individual equation: $x-8=0$ $x=8$ $x-2=0$ $x=2$ Check your answers by substituting them into the original equation: $x=8$ $8-\sqrt{2(8)}=4$ $4=4$ True $x=2$ $2-\sqrt{2(2)}=4$ $0\ne4$ False The final answer is $x=8$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.