Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises - Page 148: 78


$\color{blue}{\left\{-\dfrac{64}{3}, 4\right\}}$

Work Step by Step

Raise both sides to the 4th power to obtain: $((3x^2+52x)^{1/4})^4=4^4 \\3x^2+52x=256 \\3x^2+52x-256=0$ Factor the trinomial to obtain: $(3x+64)(x-4)=0$ Use the Zero-Factor Property by equating each factor to zero, then solve each equation to obtain: \begin{array}{ccc} &3x+64=0 &\text{or} &x-4=0 \\&3x=-64 &\text{or} &x=4 \\&x=-\frac{64}{3} &\text{or} &x=4 \end{array} Upon checking, both proposed solutions satisfy the original equation. Thus, the solution set is $\color{blue}{\left\{-\dfrac{64}{3}, 4\right\}}$.
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