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: 27

Answer

$x=\{ -1,13 \}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ (x-6)^2=49 ,$ take the square root of both sides (Square Root Property) and simplify the resulting radical. 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} x-6=\pm\sqrt{49} .\end{array} Simplifying the radical and using the properties of equality to isolate the variable result to \begin{array}{l}\require{cancel} x-6=\pm7 \\\\ x=6\pm7 .\end{array} The solutions are \begin{array}{l}\require{cancel} x=6-7 \\\\ x=-1 \\\\\text{OR}\\\\ x=6+7 \\\\ x=13 .\end{array} Hence, $ x=\{ -1,13 \} .$
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