Question

how do I solve the equation x^2+2x+8=0 and write the complex solution in standard form

Answer 1

Use the quadratic formula.
\[
x=\frac{-b\pm i \sqrt{4ac- b^2}}{2a}, \text { if } 4ac - b^2>0
\]

Answer 2

a=1, b=2, c=8
\[
4ac - b^2= 4(1)(8) - (2)^2= 32 -4= 28
\]

Answer 3

\[
x=\frac { -2 \pm i \sqrt{28}}{2}=-1 \pm i \frac{2 \sqrt 7}2\\
x_1 = -1 + \sqrt 7\ i \\
x_2 = -1 - \sqrt 7\ i \\
\]