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: 53

Answer

{$-2.52,7.52$}

Work Step by Step

Step 1: Comparing $x^{2}-5x-19=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we obtain: $a=1$, $b=-5$, and $c=-19$ 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: $x=\frac{-(-5) \pm \sqrt {(-5)^{2}-4(1)(-19)}}{2(1)}$ Step 4: $x=\frac{5 \pm \sqrt {25+76}}{2}$ Step 5: $x=\frac{5 \pm \sqrt {101}}{2}$ Step 6: $x=\frac{5 \pm 10.050}{2}$ Step 7: $x=\frac{5+10.050}{2}$ or $x=\frac{5-10.050}{2}$ Step 8: $x=\frac{15.050}{2}$ or $x=\frac{-5.050}{2}$ Step 9: $x\approx7.52$ or $x=\approx-2.52$ Step 10: Therefore, the solution set is {$-2.52,7.52$}.
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