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: 25



Work Step by Step

Step 1: Comparing $5x^{2}+3x-2=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we obtain: $a=5$, $b=3$, and $c=-2$ 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: $x=\frac{-(3) \pm \sqrt {(3)^{2}-4(5)(-2)}}{2(5)}$ Step 4: $x=\frac{-3 \pm \sqrt {9+40}}{10}$ Step 5: $x=\frac{-3 \pm \sqrt {49}}{10}$ Step 6: $x=\frac{-3 \pm 7}{10}$ Step 7: $x=\frac{-3 + 7}{10}$ or $x=\frac{-3 - 7}{10}$ Step 8: $x=\frac{4}{10}$ or $x=\frac{-10}{10}$ Step 9: $x=\frac{2}{5}$ or $x=-1$ Step 10: Therefore, the solution set is {$-1,\frac{2}{5}$}.
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