X^2+(2m-1)x-1=0

Solution for X^2+(2m-1)x-1=0 equation:

Simplifying
X2 + (2m + -1) * x + -1 = 0

Reorder the terms:
X2 + (-1 + 2m) * x + -1 = 0

Reorder the terms for easier multiplication:
X2 + x(-1 + 2m) + -1 = 0
X2 + (-1 * x + 2m * x) + -1 = 0

Reorder the terms:
X2 + (2mx + -1x) + -1 = 0
X2 + (2mx + -1x) + -1 = 0

Reorder the terms:
-1 + X2 + 2mx + -1x = 0

Solving
-1 + X2 + 2mx + -1x = 0

Solving for variable 'X'.

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

Add '1' to each side of the equation.
-1 + X2 + 2mx + 1 + -1x = 0 + 1

Reorder the terms:
-1 + 1 + X2 + 2mx + -1x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + X2 + 2mx + -1x = 0 + 1
X2 + 2mx + -1x = 0 + 1

Combine like terms: 0 + 1 = 1
X2 + 2mx + -1x = 1

Add '-2mx' to each side of the equation.
X2 + 2mx + -2mx + -1x = 1 + -2mx

Combine like terms: 2mx + -2mx = 0
X2 + 0 + -1x = 1 + -2mx
X2 + -1x = 1 + -2mx

Add 'x' to each side of the equation.
X2 + -1x + x = 1 + -2mx + x

Combine like terms: -1x + x = 0
X2 + 0 = 1 + -2mx + x
X2 = 1 + -2mx + x

Simplifying
X2 = 1 + -2mx + x

Reorder the terms:
-1 + X2 + 2mx + -1x = 1 + -2mx + x + -1 + 2mx + -1x

Reorder the terms:
-1 + X2 + 2mx + -1x = 1 + -1 + -2mx + 2mx + x + -1x

Combine like terms: 1 + -1 = 0
-1 + X2 + 2mx + -1x = 0 + -2mx + 2mx + x + -1x
-1 + X2 + 2mx + -1x = -2mx + 2mx + x + -1x

Combine like terms: -2mx + 2mx = 0
-1 + X2 + 2mx + -1x = 0 + x + -1x
-1 + X2 + 2mx + -1x = x + -1x

Combine like terms: x + -1x = 0
-1 + X2 + 2mx + -1x = 0

The solution to this equation could not be determined.