Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - Chapter 11 Review Problem Set: 57

Answer

{$-1-i\sqrt 6,-1+i\sqrt 6$}

Work Step by Step

Step 1: Comparing $n^{2}+2n+7=0$ to the standard form of a quadratic equation, $an^{2}+bn+c=0$, we find: $a=1$, $b=2$ and $c=7$ Step 2: The quadratic formula is: $n=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a, b and c in the formula: $n=\frac{-(2) \pm \sqrt {(2)^{2}-4(1)(7)}}{2(1)}$ Step 4: $n=\frac{-2 \pm \sqrt {4-28}}{2}$ Step 5: $n=\frac{-2 \pm \sqrt {-24}}{2}$ Step 6: $n=\frac{-2 \pm \sqrt {-1\times24}}{2}$ Step 7: $n=\frac{-2 \pm (\sqrt {-1}\times\sqrt {24})}{2}$ Step 8: $n=\frac{-2 \pm (i\times \sqrt {4\times6})}{2}$ Step 9: $n=\frac{-2 \pm i(2\sqrt 6)}{2}$ Step 10: $n=\frac{2(-1 \pm i\sqrt 6)}{2}$ Step 11: $n=-1 \pm i\sqrt 6$ Step 12: $n=-1-i\sqrt 6$ or $x=-1+i\sqrt 6$ Step 13: Therefore, the solution set is {$-1-i\sqrt 6,-1+i\sqrt 6$}.
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