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: 26


$\color{blue}{\left\{-\dfrac{2\sqrt{21}}{3}, \dfrac{2\sqrt{21}}{3}\right\}}$

Work Step by Step

Add $6m^2$ to both sides to obtain: \begin{align*} -6m^2+56+6m^2&=0+6m^2\\\\ 56&=6m^2\\\\ \frac{56}{6}&=m^2\\\\ \frac{28}{3}&=m^2\\\\ m^2&=\frac{28}{3} \end{align*} Take the square root of both sides to obtain: \begin{align*} \sqrt{m^2}&=\pm\sqrt{\frac{28}{3}}\\\\ m&=\pm\sqrt{\frac{4(7)}{3}}\\\\ m&=\pm\sqrt{\frac{4(7)\cdot 3}{3\cdot 3}}\\\\ m&=\pm\sqrt{\frac{4(21)}{3^2}}\\\\ m&=\pm \frac{2\sqrt{21}}{3}\\\\ \end{align*} Therefore, the solution set is $\color{blue}{\left\{-\dfrac{2\sqrt{21}}{3}, \dfrac{2\sqrt{21}}{3}\right\}}$.
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