Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises - Page 148: 94

$\{-130,59\}$

Step 1. Let $u=(x+5)^{1/3}$, we have $u^2+u-20=0$ Step 2. Factor and solve: $(u+5)(u-4)=0$ thus $u=-5,4$ Step 3. For $u=-5$, we have $(x+5)^{1/3}=-5$ or $x+5=-125$ thus $x=-130$ Step 4. For $u=4$, we have $(x+5)^{1/3}=4$ or $x+5=64$ thus $x=59$ Step 5. Solution set $\{-130,59\}$