X^2+2xy-y^2+x=2

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Solution for X^2+2xy-y^2+x=2 equation: 


Simplifying
X2 + 2xy + -1y2 + x = 2

Reorder the terms:
X2 + x + 2xy + -1y2 = 2

Solving
X2 + x + 2xy + -1y2 = 2

Solving for variable 'X'.

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

Add '-1x' to each side of the equation.
X2 + x + 2xy + -1x + -1y2 = 2 + -1x

Reorder the terms:
X2 + x + -1x + 2xy + -1y2 = 2 + -1x

Combine like terms: x + -1x = 0
X2 + 0 + 2xy + -1y2 = 2 + -1x
X2 + 2xy + -1y2 = 2 + -1x

Add '-2xy' to each side of the equation.
X2 + 2xy + -2xy + -1y2 = 2 + -1x + -2xy

Combine like terms: 2xy + -2xy = 0
X2 + 0 + -1y2 = 2 + -1x + -2xy
X2 + -1y2 = 2 + -1x + -2xy

Add 'y2' to each side of the equation.
X2 + -1y2 + y2 = 2 + -1x + -2xy + y2

Combine like terms: -1y2 + y2 = 0
X2 + 0 = 2 + -1x + -2xy + y2
X2 = 2 + -1x + -2xy + y2

Simplifying
X2 = 2 + -1x + -2xy + y2

Reorder the terms:
-2 + X2 + x + 2xy + -1y2 = 2 + -1x + -2xy + y2 + -2 + x + 2xy + -1y2

Reorder the terms:
-2 + X2 + x + 2xy + -1y2 = 2 + -2 + -1x + x + -2xy + 2xy + y2 + -1y2

Combine like terms: 2 + -2 = 0
-2 + X2 + x + 2xy + -1y2 = 0 + -1x + x + -2xy + 2xy + y2 + -1y2
-2 + X2 + x + 2xy + -1y2 = -1x + x + -2xy + 2xy + y2 + -1y2

Combine like terms: -1x + x = 0
-2 + X2 + x + 2xy + -1y2 = 0 + -2xy + 2xy + y2 + -1y2
-2 + X2 + x + 2xy + -1y2 = -2xy + 2xy + y2 + -1y2

Combine like terms: -2xy + 2xy = 0
-2 + X2 + x + 2xy + -1y2 = 0 + y2 + -1y2
-2 + X2 + x + 2xy + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-2 + X2 + x + 2xy + -1y2 = 0

The solution to this equation could not be determined.

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