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: 17

Answer

{$16,18$}

Work Step by Step

Step 1: Comparing $n^{2}-34n+288=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we obtain: $a=1$, $b=-34$, and $c=288$ 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: $x=\frac{-(-34) \pm \sqrt {(-34)^{2}-4(1)(288)}}{2(1)}$ Step 4: $x=\frac{34 \pm \sqrt {1156-1152}}{2}$ Step 5: $x=\frac{34 \pm \sqrt {4}}{2}$ Step 6: $x=\frac{34 \pm 2}{2}$ Step 7: $x=\frac{34+2}{2}$ or $x=\frac{34-2}{2}$ Step 8: $x=\frac{36}{2}$ or $x=\frac{32}{2}$ Step 9: $x=18$ or $x=16$ Step 10: Therefore, the solution set is {$16,18$}.
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