[tex]x=-2\pm i\sqrt[]{6}[/tex]
1) Let's solve this quadratic equation by the Quadratic Formula Method.
2) So, we can write out the following:
[tex]\begin{gathered} x^2+4x+10=0 \\ x=\frac{-b\pm\sqrt[]{\Delta}}{2a} \\ x_{}=\frac{-4\pm\sqrt{4^2-4\cdot\:1\cdot\:10}}{2\cdot\:1} \\ x_1=\frac{-4+2\sqrt{6}i}{2}\Rightarrow\quad x_1=-2+\sqrt{6}i \\ x_2=\frac{-4-2\sqrt{6}i}{2}\Rightarrow\quad x_2=-2-\sqrt[]{6}i \end{gathered}[/tex]
Note that as the Discriminant is negative, then this quadratic yields two complex roots. Adjusting to the way the options are presented, we can state the answer is:
[tex]\quad x=-2\pm i\sqrt[]{6}[/tex]
