Elementary Algebra

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

Chapter 10 - Quadratic Equations - 10.3 - Quadratic Formula - Problem Set 10.3 - Page 453: 38


{$\frac{-4-\sqrt {11}}{5},\frac{-4+\sqrt {11}}{5}$}

Work Step by Step

Step 1: Comparing $5n^{2}+8n+1=0$ to the standard form of a quadratic equation, $an^{2}+bn+c=0$, we find: $a=5$, $b=8$ and $c=1$ Step 2: The quadratic formula is: $n=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a,b and c in the formula: $n=\frac{-(8) \pm \sqrt {(8)^{2}-4(5)(1)}}{2(5)}$ Step 4: $n=\frac{-8 \pm \sqrt {64-20}}{10}$ Step 5: $n=\frac{-8 \pm \sqrt {44}}{10}$ Step 6: $n=\frac{-8 \pm \sqrt {4\times11}}{10}$ Step 7: $n=\frac{-8 \pm 2\sqrt {11}}{10}$ Step 8: $n=\frac{-4 \pm \sqrt {11}}{5}$ Step 9: $n=\frac{-4-\sqrt {11}}{5}$ or $n=\frac{-4+\sqrt {11}}{5}$ Step 10: Therefore, the solution set is {$\frac{-4-\sqrt {11}}{5},\frac{-4+\sqrt {11}}{5}$}.
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