Answer:
B
Step-by-step explanation:
Let u = (x-5). Now the equation becomes a quadratic in u:
u² +3u +9 = 0
Using the quadratic formula, we have a=1, b=3, c=9 and ...
[tex]u=\dfrac{-b\mp\sqrt{b^2-4ac}}{2a}=\dfrac{-3\pm\sqrt{3^2-4(1)(9)}}{2(1)}=\dfrac{-3\pm\sqrt{-27}}{2}\\\\x-5=\dfrac{-3\pm3i\sqrt{3}}{2}\qquad\text{substitute for u}\\\\\boxed{x=\dfrac{7\pm3i\sqrt{3}}{2}}\qquad\text{add 5; matches choice B}[/tex]
