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: 47


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

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: $(2n+3)^{2}=20$ Step 2: $2n+3=\pm \sqrt {20}$ Step 3: $2n+3=\pm \sqrt {4\times5}$ Step 4: $2n+3=\pm \sqrt {2^{2}\times5}$ Step 5: $2n+3=\pm 2\sqrt {5}$ Step 6: $2n+3=+ 2\sqrt {5}$ or $2n+3=-2 \sqrt {5}$ Step 7: $2n=-3+ 2\sqrt {5}$ or $2n=-3-2 \sqrt {5}$ Step 8: $n=\frac{-3+ 2\sqrt {5}}{2}$ or $n=\frac{-3- 2\sqrt {5}}{2}$ The solution set is {$\frac{-3- 2\sqrt {5}}{2},\frac{-3+ 2\sqrt {5}}{2}$}.
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