2x^2+2ix-1=0

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

Simplifying
2x2 + 2ix + -1 = 0

Reorder the terms:
-1 + 2ix + 2x2 = 0

Solving
-1 + 2ix + 2x2 = 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 + 2ix + 1 + 2x2 = 0 + 1

Reorder the terms:
-1 + 1 + 2ix + 2x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2ix + 2x2 = 0 + 1
2ix + 2x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2ix + 2x2 = 1

Add '-2x2' to each side of the equation.
2ix + 2x2 + -2x2 = 1 + -2x2

Combine like terms: 2x2 + -2x2 = 0
2ix + 0 = 1 + -2x2
2ix = 1 + -2x2

Divide each side by '2x'.
i = 0.5x-1 + -1x

Simplifying
i = 0.5x-1 + -1x