Answer
$\{3-2i,3+2i\}$
Work Step by Step
The given equation has $a=1,b=-6$ and $c=13$.
The discriminant is
$=b^2-4ac$
$=(-6)^2-4(1)(13)$
$=36-52$
$=-16$
Use Quadratic formula.
$x=\dfrac{-b\pm \sqrt {b^2-4ac}}{2a}$
Substitute the values of $a, b, c, $ and the discriminant.
$x=\dfrac{-(-6)\pm \sqrt {-16}}{2(1)}$
Simplify.
$x=\dfrac{6\pm \sqrt{16(-1)}}{2}$
$x=\dfrac{6\pm 4i}{2}$
Factor out $2$.
$x=\dfrac{2(3\pm 2i)}{2}$
Cancel common factors.
$x=3\pm 2i$
The equation has two solutions: $3-2i$ and $3+2i$.
Check:
For $x=3-2i$.
$=(3-2i)^2-6(3-2i)+13$
$=9-12i+4i^2-18+12i+13$
$=4+4i^2$
$=4-4$
$=0$
For $x=3+2i$.
$=(3+2i)^2-6(3+2i)+13$
$=9+12i+4i^2-18-12i+13$
$=4+4i^2$
$=4-4$
$=0$
Hence, the solution set is $\{3-2i,3+2i\}$.
