Elementary Algebra

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

Chapter 10 - Quadratic Equations - 10.4 - Solving Quadratic Equations - Which Method? - Problem Set 10.4: 3

Answer

{$-\frac{13}{5},\frac{1}{5}$}

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: $(5n+6)^{2}=49$ Step 2: $5n+6=\pm \sqrt {49}$ Step 3: $5n+6=\pm 7$ Step 4: $5n+6=7$ or $5n+6=-7$ Step 5: $5n=7-6$ or $5n=-7-6$ Step 6: $5n=1$ or $5n=-13$ Step 7: $n=\frac{1}{5}$ or $n=-\frac{13}{5}$ The solution set is {$-\frac{13}{5},\frac{1}{5}$}.
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