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: 18

Answer

{$-14,-13$}

Work Step by Step

Step 1: Comparing $n^{2}+27n+182=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we obtain: $a=1$, $b=27$, and $c=182$ Step 2: The quadratic formula is: $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a,b, and c in the formula, we obtain: $x=\frac{-(27) \pm \sqrt {(27)^{2}-4(1)(182)}}{2(1)}$ Step 4: $x=\frac{-27 \pm \sqrt {729-728}}{2}$ Step 5: $x=\frac{-27 \pm \sqrt {1}}{2}$ Step 6: $x=\frac{-27 \pm 1}{2}$ Step 7: $x=\frac{-27+1}{2}$ or $x=\frac{-27-1}{2}$ Step 8: $x=\frac{-26}{2}$ or $x=\frac{-28}{2}$ Step 9: $x=-13$ or $x=-14$ Step 10: Therefore, the solution set is {$-14,-13$}.
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