Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Section 9.1 - Solving Quadratic Equations by the Square Root Property - Exercise Set - Page 631: 29


$x=\left\{ 4-3\sqrt{2},4+3\sqrt{2} \right\}$

Work Step by Step

Taking the square root of both sides (the Square Root Property), the solutions to the given equation, $ (z-4)^2=18 ,$ are \begin{array}{l}\require{cancel} z-4=\pm\sqrt{18} \\\\ z-4=\pm\sqrt{9\cdot2} \\\\ z-4=\pm\sqrt{(3)^2\cdot2} \\\\ z-4=\pm3\sqrt{2} \\\\ z=4\pm3\sqrt{2} .\end{array} Hence, $ x=\left\{ 4-3\sqrt{2},4+3\sqrt{2} \right\} .$
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