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: 8

Answer

{$-4-2i\sqrt {7},-4+2i\sqrt {7}$}

Work Step by Step

We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain: Step 1: $(x+4)^{2}=-28$ Step 2: $x+4=\pm \sqrt {-28}$ Step 3: $x+4=\pm \sqrt {-1\times4\times7}$ Step 4: $x+4=\pm (\sqrt {-1}\times\sqrt {4}\times\sqrt 7)$ Step 5: $x+4=\pm (i\times2\times\sqrt {7})$ [as $i=\sqrt {-1}$] Step 6: $x+4=\pm (2i\sqrt {7})$ Step 7: $x=-4\pm (2i\sqrt {7})$ Step 8: $x=-4+2i\sqrt {7}$ or $x=-4-2i\sqrt {7}$ Therefore, the solution set is {$-4-2i\sqrt {7},-4+2i\sqrt {7}$}.
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