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