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: 30


{$\frac{-3 - \sqrt {33}}{4}\frac{-3 + \sqrt {33}}{4}$}

Work Step by Step

Step 1: Comparing $2x^{2}+3x-3=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=2$, $b=3$ and $c=-3$ 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: $x=\frac{-(3) \pm \sqrt {(3)^{2}-4(2)(-3)}}{2(2)}$ Step 4: $x=\frac{-3 \pm \sqrt {9+24}}{4}$ Step 5: $x=\frac{-3 \pm \sqrt {33}}{4}$ Step 6: $x=\frac{-3 - \sqrt {33}}{4}$ or $x=\frac{-3 + \sqrt {33}}{4}$ Step 7: Therefore, the solution set is {$\frac{-3 - \sqrt {33}}{4},\frac{-3 + \sqrt {33}}{4}$}.
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