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: 35

Answer

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

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: $8n^{2}=25$ Step 2: $n^{2}=\frac{25}{8}$ Step 3: $x=\pm \sqrt {\frac{25}{8}}$ Step 4: $x=\pm \frac{\sqrt {25}}{\sqrt 8}$ Step 5: $x=\pm \frac{\sqrt {25}}{\sqrt {4\times2}}$ Step 6: $x=\pm \frac{5}{2\sqrt 2}$ Step 7: $x=\pm \frac{5}{2\sqrt 2}\times\frac{2\sqrt 2}{2\sqrt 2}$ Step 8: $x=\pm \frac{10\sqrt 2}{(2\sqrt 2)^{2}}$ Step 9: $x=\pm \frac{10\sqrt 2}{4 \times 2}$ Step 10: $x=\pm \frac{5\sqrt 2}{4}$ The solution set is {$- \frac{5\sqrt 2}{4}, \frac{5\sqrt 2}{4}$}.
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