## Trigonometry (11th Edition) Clone

The solution set of this problem is $$\Big\{-2\pm i\sqrt7\Big\}$$
$$x^2+4x+11=0$$ 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 $$\Big\{-2\pm i\sqrt7\Big\}$$