Answer:
C
Step-by-step explanation:
We want to solve the equation:
[tex]x^2+2x+7=0[/tex]
Using the quadratic formula. The quadratic formula is given by:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = 2, and c = 7.
Substitute:
[tex]\displaystyle x=\frac{-(2)\pm\sqrt{(2)^2-4(1)(7)}}{2(1)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{-2\pm\sqrt{-24}}{2}[/tex]
Simplify the square root:
[tex]\sqrt{-24}=\sqrt{4\cdot 6\cdot -1}=\sqrt{4}\cdot\sqrt{6}\cdot\sqrt{-1}=2i\sqrt{6}[/tex]
Hence:
[tex]\displaystyle x=\frac{-2\pm2i\sqrt{6}}{2}[/tex]
Simplify:
[tex]\displaystyle x=-1\pm i\sqrt{6}[/tex]
Hence, our solutions are:
[tex]\displaystyle x=\left\{-1+i\sqrt{6}, -1-i\sqrt{6}\right\}[/tex]
Our answer is C.
