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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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