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: 24

Answer

{$-4 - 2i\sqrt 2,-4 + 2i\sqrt 2$}

Work Step by Step

Step 1: Comparing $y^{2}+8y+24=0$ to the standard form of a quadratic equation, $ay^{2}+by+c=0$, we find: $a=1$, $b=8$ and $c=24$ Step 2: The quadratic formula is: $y=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a, b and c in the formula: $y=\frac{-(8) \pm \sqrt {(8)^{2}-4(1)(24)}}{2(1)}$ Step 4: $y=\frac{-8 \pm \sqrt {64-96}}{2}$ Step 5: $y=\frac{-8 \pm \sqrt {-32}}{2}$ Step 6: $y=\frac{-8 \pm \sqrt {-1\times32}}{2}$ Step 7: $y=\frac{-8 \pm (\sqrt {-1}\times\sqrt {32})}{2}$ Step 8: $y=\frac{-8 \pm (\sqrt {-1}\times\sqrt {16\times2})}{2}$ Step 9: $y=\frac{-8 \pm (i\times 4\sqrt 2)}{2}$ Step 10: $y=\frac{-8 \pm 4i\sqrt 2}{2}$ Step 11: $y=\frac{2(-4 \pm 2i\sqrt 2)}{2}$ Step 12: $y=-4 \pm 2i\sqrt 2$ Step 13: $y=-4 - 2i\sqrt 2$ or $y=-4 + 2i\sqrt 2$ Step 14: Therefore, the solution set is {$-4 - 2i\sqrt 2,-4 + 2i\sqrt 2$}.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.