Question

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answer 1

Answer:

C

Step-by-step explanation:

We want to solve the equation:

$x^2+2x+7=0$

Using the quadratic formula. The quadratic formula is given by:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a = 1, b = 2, and c = 7.

Substitute:

$\displaystyle x=\frac{-(2)\pm\sqrt{(2)^2-4(1)(7)}}{2(1)}$

Evaluate:

$\displaystyle x=\frac{-2\pm\sqrt{-24}}{2}$

Simplify the square root:

$\sqrt{-24}=\sqrt{4\cdot 6\cdot -1}=\sqrt{4}\cdot\sqrt{6}\cdot\sqrt{-1}=2i\sqrt{6}$

Hence:

$\displaystyle x=\frac{-2\pm2i\sqrt{6}}{2}$

Simplify:

$\displaystyle x=-1\pm i\sqrt{6}$

Hence, our solutions are:

$\displaystyle x=\left\{-1+i\sqrt{6}, -1-i\sqrt{6}\right\}$

Our answer is C.