Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises - Page 148: 61

$\{-2\}$

Step 1. Rewrite the equation as $\sqrt {3x+7}=1-\sqrt {x+2}$ Step 2. Take square on both sides to get: $3x+7=1-2\sqrt {x+2}+x+2$ or $x+2=-\sqrt {x+2}$ Step 3. Take square on both sides again to get: $x^2+4x+4=x+2$ or $x^2+3x+2=0$ which gives $x=-1,-2$ Step 4. Check answer in the original equation: only $\{-2\}$ fits.