Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - Chapter 11 Review Problem Set: 63

Answer

{$\frac{-3 - i\sqrt {39}}{4},\frac{-3 + i\sqrt {39}}{4}$}

Work Step by Step

Step 1: Comparing $-2x^{2}-3x-6=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=-2$, $b=-3$ 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: $x=\frac{-(-3) \pm \sqrt {(-3)^{2}-4(-2)(-6)}}{2(-2)}$ Step 4: $x=\frac{3 \pm \sqrt {9-48}}{-4}$ Step 5: $x=\frac{3 \pm \sqrt {-39}}{-4}$ Step 6: $x=\frac{3 \pm \sqrt {-1\times39}}{-4}$ Step 7: $x=\frac{3 \pm (\sqrt {-1}\times\sqrt {39})}{-4}$ Step 8: $x=\frac{3 \pm (i\times \sqrt {39})}{-4}$ Step 9: $x=\frac{3 \pm i\sqrt {39}}{-4}$ Step 10: $x=\frac{3 - i\sqrt {39}}{-4}$ or $x=\frac{3 + i\sqrt {39}}{-4}$ Step 11: $x=\frac{-(3 - i\sqrt {39})}{4}$ or $x=\frac{-(3 + i\sqrt {39})}{4}$ Step 12: Therefore, the solution set is {$\frac{-3 - i\sqrt {39}}{4},\frac{-3 + i\sqrt {39}}{4}$}.
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