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: 5

Answer

{$-5-i\sqrt {13},-5+i\sqrt {13}$}

Work Step by Step

We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain: Step 1: $(x+5)^{2}=-13$ Step 2: $x+5=\pm \sqrt {-13}$ Step 3: $x+5=\pm \sqrt {-1\times13}$ Step 4: $x+5=\pm (\sqrt {-1}\times\sqrt {13})$ Step 5: $x+5=\pm (i\times\sqrt {13})$ [as $i=\sqrt {-1}$] Step 6: $x+5=\pm (i\sqrt {13})$ Step 7: $x=-5\pm (i\sqrt {13})$ Step 8: $x=-5+i\sqrt {13}$ or $x=-5-i\sqrt {13}$ Therefore, the solution set is {$-5-i\sqrt {13},-5+i\sqrt {13}$}.
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.