Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Review: 158

Answer

$x=4$

Work Step by Step

Using the properties of equality, the given equation, $ \sqrt{x}+2=x ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{x}=x-2 .\end{array} Raising both sides to the second power, then the solution/s to the equation above is/are \begin{array}{l}\require{cancel} x=(x-2)^2 \\\\ x=(x)^2+2(x)(-2)+(-2)^2 \\\\ x=x^2-4x+4 \\\\ -x^2+(x+4x)-4=0 \\\\ -x^2+5x-4=0 \\\\ x^2-5x+4=0 \\\\ (x-4)(x-1)=0 \\\\ x=\left\{ 1,4 \right\} .\end{array} Upon checking, only $ x=4 $ satisfies the original equation.
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