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: 43


{$\frac{-5-\sqrt {137}}{14},\frac{-5+\sqrt {137}}{14}$}

Work Step by Step

Step 1: Comparing $7x^{2}+5x-4=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=7$, $b=5$ and $c=-4$ 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: $x=\frac{-(5) \pm \sqrt {(5)^{2}-4(7)(-4)}}{2(7)}$ Step 4: $x=\frac{-5 \pm \sqrt {25+112}}{14}$ Step 5: $x=\frac{-5 \pm \sqrt {137}}{14}$ Step 6: $x=\frac{-5-\sqrt {137}}{14}$ or $x=\frac{-5+\sqrt {137}}{14}$ Step 7: Therefore, the solution set is {$\frac{-5-\sqrt {137}}{14},\frac{-5+\sqrt {137}}{14}$}.
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