Elementary Algebra

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

Chapter 10 - Quadratic Equations - 10.1 - Quadratic Equations - Problem Set 10.1: 31

Answer

{$-3\sqrt 2, 3\sqrt 2$}

Work Step by Step

Using Property 10.1, which states that for any non-negative real number $a$, $x^{2}=a$ can be written as $x=\pm\sqrt a$, we obtain: Step 1: $3x^{2}-54=0$ Step 2: $3x^{2}=54$ Step 3: $x^{2}=\frac{54}{3}$ Step 4: $x^{2}=18$ Step 5: $x=\pm \sqrt {18}$ Step 6: $x=\pm \sqrt {9\times 2}$ Step 7: $x=\pm (\sqrt {9}\times \sqrt 2)$ Step 8: $x=\pm (3\times \sqrt 2)$ Step 9: $x=\pm 3\sqrt 2$ The solution set is {$-3\sqrt 2, 3\sqrt 2$}.
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