Answer
$ 18$
Work Step by Step
$\sqrt {3x-5}-\sqrt {x+7}=2$
$\sqrt {3x-5}=\sqrt {x+7}+2$
$3x-5=x+7+4\sqrt {x+7}+4$
$2x-16=4\sqrt {x+7}$
$x-8=2\sqrt {x+7}$
$x^2-16x+64=4x+28$
$x^2-20x+36=0$
$(x-2)(x-18)=0$
$x=2,18$
Check, only $x=18$ fits.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Appendix A - Review - A.8 Solving Equations - A.8 Assess Your Understanding - Page A70: 58
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