X^2+2xy-2y^2+x+y+1=0

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Solution for X^2+2xy-2y^2+x+y+1=0 equation:


Simplifying
X2 + 2xy + -2y2 + x + y + 1 = 0

Reorder the terms:
1 + X2 + x + 2xy + y + -2y2 = 0

Solving
1 + X2 + x + 2xy + y + -2y2 = 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 + x + 2xy + y + -1 + -2y2 = 0 + -1

Reorder the terms:
1 + -1 + X2 + x + 2xy + y + -2y2 = 0 + -1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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