Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - 8.1 Exercises: 91

Answer

$x=\dfrac{2b\pm\sqrt{3a}}{5}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To find the solutions of the given equation, $ (5x-2b)^2=3a ,$ take the square root of both sides ((Square Root Property). Then use the properties of equality to isolate $x.$ $\bf{\text{Solution Details:}}$ Taking the square root of both sides and then simplifying the radical, the equation above is equivalent to \begin{array}{l}\require{cancel} 5x-2b=\pm\sqrt{3a} .\end{array} Using the properties of equality to isolate $x$, the given equation is equivalent to \begin{array}{l}\require{cancel} 5x=2b\pm\sqrt{3a} \\\\ x=\dfrac{2b\pm\sqrt{3a}}{5} .\end{array}
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