Answer
$ -5+3j, \ or, \ -5-3j .$
Work Step by Step
For the equation $x^2 +10x+34 = 0$, we use the quadratic formula as follows
$$ x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}, \\
a=1, \quad b=10, \quad c=34 .$$
That is,
$$ x=\frac{-10 \pm \sqrt{100-4(34)}}{2 }= -5+3j, \ or, \ -5-3j .$$
