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: 37


{$\frac{-9-\sqrt {57}}{12},\frac{-9+\sqrt {57}}{12}$}

Work Step by Step

Step 1: Comparing $6n^{2}+9n+1=0$ to the standard form of a quadratic equation, $an^{2}+bn+c=0$, we find: $a=6$, $b=9$ 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: $n=\frac{-(9) \pm \sqrt {(9)^{2}-4(6)(1)}}{2(6)}$ Step 4: $n=\frac{-9 \pm \sqrt {81-24}}{12}$ Step 5: $n=\frac{-9 \pm \sqrt {57}}{12}$ Step 6: $n=\frac{-9-\sqrt {57}}{12}$ or $n=\frac{-9+\sqrt {57}}{12}$ Step 7: Therefore, the solution set is {$\frac{-9-\sqrt {57}}{12},\frac{-9+\sqrt {57}}{12}$}.
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