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: 34

Answer

$x=\left\{ \dfrac{5-\sqrt{10}}{2},\dfrac{5+\sqrt{10}}{2} \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ (2x-5)^2=10 ,$ take the square root of both sides (Square Root Property). Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Taking the square root of both sides (Square Root Property), the equation above is equivalent to \begin{array}{l}\require{cancel} 2x-5=\pm\sqrt{10} .\end{array} Using the properties of equality to isolate the variable, the equation above is equivalent to \begin{array}{l}\require{cancel} 2x=5\pm\sqrt{10} \\\\ x=\dfrac{5\pm\sqrt{10}}{2} .\end{array} The solutions are \begin{array}{l}\require{cancel} x=\dfrac{5-\sqrt{10}}{2} \\\\\text{OR}\\\\ x=\dfrac{5+\sqrt{10}}{2} .\end{array} Hence, $ x=\left\{ \dfrac{5-\sqrt{10}}{2},\dfrac{5+\sqrt{10}}{2} \right\} .$
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