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: 13

Answer

{$-3 - i\sqrt 3,-3 + i\sqrt 3$}

Work Step by Step

Step 1: Comparing $t^{2}+6t+12=0$ to the standard form of a quadratic equation, $at^{2}+bt+c=0$, we find: $a=1$, $b=6$ and $c=12$ 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: $x=\frac{-(6) \pm \sqrt {(6)^{2}-4(1)(12)}}{2(1)}$ Step 4: $x=\frac{-6 \pm \sqrt {36-48}}{2}$ Step 5: $x=\frac{-6 \pm \sqrt {-12}}{2}$ Step 6: $x=\frac{-6 \pm \sqrt {-1\times12}}{2}$ Step 7: $x=\frac{-6 \pm (\sqrt {-1}\times\sqrt {4\times3})}{2}$ Step 8: $x=\frac{-6 \pm (i\times 2\sqrt 3)}{2}$ Step 9: $x=\frac{-6 \pm i2\sqrt 3}{2}$ Step 10: $x=\frac{2(-3 \pm i\sqrt 3)}{2}$ Step 11: $x=-3 \pm i\sqrt 3$ Step 12: $x=-3 - i\sqrt 3$ or $x=-3 + i\sqrt 3$ Step 13: Therefore, the solution set is {$-3 - i\sqrt 3,-3 + i\sqrt 3$}.
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