Elementary Algebra

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

Chapter 11 - Additional Topics - 11.5 - Quadratic Equations: Complex Solutions - Problem Set 11.5: 9

Answer

{$-\frac{2}{5},\frac{4}{5}$}

Work Step by Step

We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain: Step 1: $(5x-1)^{2}=9$ Step 2: $5x-1=\pm \sqrt {9}$ Step 3: $5x-1=\pm 3$ Step 4: $5x=1\pm 3$ Step 5: $x=\frac{1\pm 3}{5}$ Step 6: $x=\frac{1+ 3}{5}$ or $x=\frac{1- 3}{5}$ Step 7: $x=\frac{4}{5}$ or $x=\frac{-2}{5}$ Therefore, the solution set is {$-\frac{2}{5},\frac{4}{5}$}.
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