Answer
{$\frac{3 - i\sqrt {11}}{2},\frac{3 + i\sqrt {11}}{2}$}
Work Step by Step
Step 1: Comparing $x^{2}-3x+5=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find:
$a=1$, $b=-3$ and $c=5$
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:
$x=\frac{-(-3) \pm \sqrt {(-3)^{2}-4(1)(5)}}{2(1)}$
Step 4: $x=\frac{3 \pm \sqrt {9-20}}{2}$
Step 5: $x=\frac{3 \pm \sqrt {-11}}{2}$
Step 6: $x=\frac{3 \pm \sqrt {-1\times11}}{2}$
Step 7: $x=\frac{3 \pm (\sqrt {-1}\times\sqrt {11})}{2}$
Step 8: $x=\frac{3 \pm (i\times \sqrt {11})}{2}$
Step 9: $x=\frac{3 \pm i\sqrt {11}}{2}$
Step 10: $x=\frac{3 - i\sqrt {11}}{2}$ or $x=\frac{3 + i\sqrt {11}}{2}$
Step 11: Therefore, the solution set is {$\frac{3 - i\sqrt {11}}{2},\frac{3 + i\sqrt {11}}{2}$}.
