Answer
$\{-2-2i,-2+2i\}$
Work Step by Step
The given equation has $a=1,b=4$ and $c=8$.
The discriminant is
$=b^2-4ac$
$=(4)^2-4(1)(8)$
$=16-32$
$=-16$
Use Quadratic formula.
$x=\dfrac{-b\pm \sqrt {b^2-4ac}}{2a}$
Substitute the values of $a, b, c, $ and the discriminant.
$x=\dfrac{-(4)\pm \sqrt {-16}}{2(1)}$
Simplify.
$x=\dfrac{-4\pm \sqrt{16(-1)}}{2}$
$x=\dfrac{-4\pm 4i}{2}$
Factor out $2$.
$x=\dfrac{2(-2\pm 2i)}{2}$
Cancel common factor $2$.
$x=-2\pm 2i$
The equation has two solutions: $-2-2i$ and $-2+2i$.
Check:
For $x=-2-2i$.
$=(-2-2i)^2+4(-2-2i)+8$
$=4+8i+4i^2-8-8i+8$
$=4+4i^2$
$=4-4$
$=0$
For $x=-2+2i$.
$=(-2+2i)^2+4(-2+2i)+8$
$=4-8i+4i^2-8+8i+8$
$=4+4i^2$
$=4-4$
$=0$
Hence, the solution set is $\{-2-2i,-2+2i\}$.
