we have the quadratic equation
x^2+8x+52=0
using the formula to solve the quadratic equation
a=1
b=8
c=52
substitute the given values in the formula
[tex]x=\frac{-8\pm\sqrt[]{8^2-4(1)(52)}}{2(1)}[/tex][tex]x=\frac{-8\pm\sqrt[]{-144}}{2}[/tex]Remember that
i^2=-1
144=12^2
so
[tex]x=\frac{-8\pm12i}{2}[/tex]Simplify
[tex]x=-4\pm6i[/tex]