Answer
$\{3-i,3+i\}$
Work Step by Step
The given equation is in standard form where $a=1,b=-6$ and $c=10$.
The discriminant is
$=b^2-4ac$
$=(-6)^2-4(1)(10)$
$=36-40$
$=-4$
Use Quadratic formula.
$x=\dfrac{-b\pm \sqrt {b^2-4ac}}{2a}$
Substitute the values of $a, b, c, $ and the discriminant.
$x=\dfrac{-(-6)\pm \sqrt {(-4)}}{2(1)}$
Simplify.
$x=\dfrac{6\pm \sqrt{4(-1)}}{2}$
$x=\dfrac{6\pm 2i}{2}$
Factor out $2$.
$x=\dfrac{2(3\pm i)}{2}$
Cancel the common factor $2$.
$x=3\pm i$
The equation has two solutions: $3-i$ and $3+i$.
Check:
For $x=3-i$.
$=(3-i)^2-6(3-i)+10$
$=9-6i+i^2-18+6i+10$
$=1+i^2$
$=1-1$
$=0$
For $x=3+i$.
$=(3+i)^2-6(3+i)+10$
$=9+6i+i^2-18-6i+10$
$=1+i^2$
$=1-1$
$=0$
Hence, the solution set is $\{3-i,3+i\}$.
