Answer
The solution set of this problem is $$\Big\{-2\pm i\sqrt7\Big\}$$
Work Step by Step
$$x^2+4x+11=0$$
The equation is already in standard form, so the quadratic formula can immediately be used.
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
As $a=1, b=4, c=11$
$$x=\frac{-4\pm\sqrt{4^2-4\times1\times11}}{2\times1}$$
$$x=\frac{-4\pm\sqrt{16-44}}{2}$$
$$x=\frac{-4\pm\sqrt{-28}}{2}$$
Now we rewrite $\sqrt{-28}=i\sqrt{28}=2i\sqrt7$
$$x=\frac{-4\pm 2i\sqrt7}{2}$$
Then we simplify
$$x=-2\pm i\sqrt7$$
The solution set of this problem is $$\Big\{-2\pm i\sqrt7\Big\}$$
