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: 62

Answer

{$\frac{5 - i\sqrt {3})}{2},\frac{5 + i\sqrt {3})}{2}$}

Work Step by Step

Step 1: Comparing $-x^{2}+5x-7=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=-1$, $b=5$ and $c=-7$ Step 2: The quadratic formula is: $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a, b and c in the formula: $x=\frac{-(5) \pm \sqrt {(5)^{2}-4(-1)(-7)}}{2(-1)}$ Step 4: $x=\frac{-5 \pm \sqrt {25-28}}{-2}$ Step 5: $x=\frac{-5 \pm \sqrt {-3}}{-2}$ Step 6: $x=\frac{-5 \pm \sqrt {-1\times3}}{-2}$ Step 7: $x=\frac{-5 \pm (\sqrt {-1}\times\sqrt {3})}{-2}$ Step 8: $x=\frac{-5 \pm (i\times \sqrt {3})}{-2}$ Step 9: $x=\frac{-5 \pm i\sqrt {3}}{-2}$ Step 10: $x=\frac{-5 - i\sqrt {3}}{-2}$ or $x=\frac{-5 + i\sqrt {3}}{-2}$ Step 11: $x=\frac{-(-5 - i\sqrt {3})}{2}$ or $x=\frac{-(-5 + i\sqrt {3})}{2}$ Step 12: $x=\frac{5 + i\sqrt {3})}{2}$ or $x=\frac{5 - i\sqrt {3})}{2}$ Step 13: Therefore, the solution set is {$\frac{5 - i\sqrt {3})}{2},\frac{5 + i\sqrt {3})}{2}$}.
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