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: 30

Answer

$x=\left\{ 6-2\sqrt{3},6+2\sqrt{3} \right\}$

Work Step by Step

Taking the square root of both sides (the Square Root Property), the solutions to the given equation, $ (z-6)^2=12 ,$ are \begin{array}{l}\require{cancel} z-6=\pm\sqrt{12} \\\\ z-6=\pm\sqrt{4\cdot3} \\\\ z-6=\pm\sqrt{(2)^2\cdot3} \\\\ z-6=\pm2\sqrt{3} \\\\ z=6\pm2\sqrt{3} .\end{array} Hence, $ x=\left\{ 6-2\sqrt{3},6+2\sqrt{3} \right\} .$
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