Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 4 - Quadratic Functions - 4.6 Solving Quadratic Equations by Using the Quadratic Formula - 4.6 Exercises - Page 373: 28


$\color{blue}{\left\{-\frac{3}{2}, 0\right\}}$

Work Step by Step

Factor out $\dfrac{1}{5}x$ to obtain: \begin{align*} \frac{1}{5}x\left(2x+3\right)&=0 \end{align*} Use the Zero-Product Property by equating each factor to zero. Then, solve each equation to obtain: \begin{align*} \frac{1}{5}x&=0 &\text{or}& &2x+3&=0\\\\ x&=0 &\text{or}& &2x=-3\\\\ x&=0 &\text{or}& &x=-\frac{3}{2}\\\\ \end{align*} Therefore, the solution set is $\color{blue}{\left\{-\frac{3}{2}, 0\right\}}$.
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