Answer
$ -2$
Work Step by Step
$\sqrt {3x+7}+\sqrt {x+2}=1$
$\sqrt {3x+7}=1-\sqrt {x+2}$
$3x+7=1-2\sqrt {x+2}+x+2$
$2x+4=2\sqrt {x+2}$
$x+2=\sqrt {x+2}$
$x^2+4x+4=x+2$
$x^2+3x+2=0$
$(x+2)(x+1)=0$
$x=-1,-2$
Check, only $x=-2$ 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: 56
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