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: 48


{$\frac{2- 2\sqrt {7}}{3},\frac{2+2\sqrt {7}}{3}$}

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: $(3n-2)^{2}=28$ Step 2: $3n-2=\pm \sqrt {28}$ Step 3: $3n-2=\pm \sqrt {4\times7}$ Step 4: $3n-2=\pm \sqrt {2^{2}\times7}$ Step 5: $3n-2=\pm 2\sqrt {7}$ Step 6: $3n-2=+ 2\sqrt {7}$ or $3n-2=-2 \sqrt {7}$ Step 7: $3n=2+ 2\sqrt {7}$ or $3n=2-2 \sqrt {7}$ Step 8: $n=\frac{2+ 2\sqrt {7}}{3}$ or $n=\frac{2- 2\sqrt {7}}{3}$ The solution set is {$\frac{2- 2\sqrt {7}}{3},\frac{2+2\sqrt {7}}{3}$}.
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