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: 33



Work Step by Step

Step 1: Comparing $16x^{2}+24x+9=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=16$, $b=24$ and $c=9$ 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: $x=\frac{-(24) \pm \sqrt {(24)^{2}-4(16)(9)}}{2(16)}$ Step 4: $x=\frac{-24 \pm \sqrt {576-576}}{32}$ Step 5: $x=\frac{-24 \pm \sqrt {0}}{32}$ Step 6: $x=\frac{-24 \pm 0}{32}$ Step 7: $x=\frac{-24}{32}$ Step 8: $x=\frac{-3}{4}$ Step 9: Therefore, the solution set is {$-\frac{3}{4}$}.
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