Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 10 - Quadratic Equations - Chapter 10 Review Problem Set - Page 467: 11


{$2-\sqrt 2,2+\sqrt 2$}

Work Step by Step

Using Property 10.1, which says that for any non-negative real number $a$, $x^{2}=a$ can be written as $x=\pm\sqrt a$, we obtain: Step 1: $3(x-2)^{2}-2=4$ Step 2: $3(x-2)^{2}=4+2$ Step 3: $3(x-2)^{2}=6$ Step 4: $(x-2)^{2}=\frac{6}{3}$ Step 5: $(x-2)^{2}=2$ Step 6: $x-2=\pm \sqrt {2}$ Step 7: $x=2\pm \sqrt 2$ Step 8: $x=2+ \sqrt 2$ or $x=2- \sqrt 2$ The solution set is {$2-\sqrt 2,2+\sqrt 2$}.
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