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: 28

Answer

{$\frac{-7 + \sqrt {97}}{4},\frac{-7 - \sqrt {97}}{4}$}

Work Step by Step

Step 1: Comparing $2x^{2}+7x-6=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we obtain: $a=2$, $b=7$, and $c=-6$ 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: $x=\frac{-(7) \pm \sqrt {(7)^{2}-4(2)(-6)}}{2(2)}$ Step 4: $x=\frac{-7 \pm \sqrt {49+48}}{4}$ Step 5: $x=\frac{-7 \pm \sqrt {97}}{4}$ Step 6: $x=\frac{-7 + \sqrt {97}}{4}$ or $x=\frac{-7 - \sqrt {97}}{4}$ Step 7: Therefore, the solution set is {$\frac{-7 + \sqrt {97}}{4},\frac{-7 - \sqrt {97}}{4}$}.
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