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: 6

Answer

{$7-i\sqrt {21},7+i\sqrt {21}$}

Work Step by Step

We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain: Step 1: $(x-7)^{2}=-21$ Step 2: $x-7=\pm \sqrt {-21}$ Step 3: $x-7=\pm \sqrt {-1\times21}$ Step 4: $x-7=\pm (\sqrt {-1}\times\sqrt {21})$ Step 5: $x-7=\pm (i\times\sqrt {21})$ [as $i=\sqrt {-1}$] Step 6: $x-7=\pm (i\sqrt {21})$ Step 7: $x=7\pm (i\sqrt {21})$ Step 8: $x=7+i\sqrt {21}$ or $x=7-i\sqrt {21}$ Therefore, the solution set is {$7-i\sqrt {21},7+i\sqrt {21}$}.
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