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: 51


{$\frac{5- 2\sqrt {10}}{3},\frac{5+ 2\sqrt {10}}{3}$}

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: $(3x-5)^{2}=40$ Step 2: $3x-5=\pm \sqrt {40}$ Step 3: $3x-5=\pm \sqrt {4\times10}$ Step 4: $3x-5=\pm \sqrt {2^{2}\times10}$ Step 5: $3x-5=\pm 2\sqrt {10}$ Step 6: $3x-5=+ 2\sqrt {10}$ or $3x-5=-2 \sqrt {10}$ Step 7: $3x=5+ 2\sqrt {10}$ or $3x=5-2 \sqrt {10}$ Step 8: $x=\frac{5+ 2\sqrt {10}}{3}$ or $x=\frac{5- 2\sqrt {10}}{3}$ The solution set is {$\frac{5- 2\sqrt {10}}{3},\frac{5+ 2\sqrt {10}}{3}$}.
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