x^2+ix+1=0

Solution for x^2+ix+1=0 equation:

Simplifying
x2 + ix + 1 = 0

Reorder the terms:
1 + ix + x2 = 0

Solving
1 + ix + x2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + ix + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + ix + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + ix + x2 = 0 + -1
ix + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
ix + x2 = -1

Add '-1x2' to each side of the equation.
ix + x2 + -1x2 = -1 + -1x2

Combine like terms: x2 + -1x2 = 0
ix + 0 = -1 + -1x2
ix = -1 + -1x2

Divide each side by 'x'.
i = -1x-1 + -1x

Simplifying
i = -1x-1 + -1x