Elementary Algebra

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

Chapter 11 - Additional Topics - 11.5 - Quadratic Equations: Complex Solutions - Problem Set 11.5: 30

Answer

{$\frac{-3 - 5i\sqrt {3}}{14},\frac{-3 + 5i\sqrt {3}}{14}$}

Work Step by Step

Step 1: Comparing $7x^{2}+3x+3=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=7$, $b=3$ 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: $x=\frac{-(3) \pm \sqrt {(3)^{2}-4(7)(3)}}{2(7)}$ Step 4: $x=\frac{-3 \pm \sqrt {9-84}}{14}$ Step 5: $x=\frac{-3 \pm \sqrt {-75}}{14}$ Step 6: $x=\frac{-3 \pm \sqrt {-1\times75}}{14}$ Step 7: $x=\frac{-3 \pm (\sqrt {-1}\times\sqrt {25\times3})}{14}$ Step 8: $x=\frac{-3 \pm (i\times 5\sqrt {3})}{14}$ Step 9: $x=\frac{-3 \pm i5\sqrt {3}}{14}$ Step 10: $x=\frac{-3 - 5i\sqrt {3}}{14}$ or $x=\frac{-3 + 5i\sqrt {3}}{14}$ Step 11: Therefore, the solution set is {$\frac{-3 - 5i\sqrt {3}}{14},\frac{-3 + 5i\sqrt {3}}{14}$}.
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