X^2-2xy+y^2=6x-4y+1

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Solution for X^2-2xy+y^2=6x-4y+1 equation: 


Simplifying
X2 + -2xy + y2 = 6x + -4y + 1

Reorder the terms:
X2 + -2xy + y2 = 1 + 6x + -4y

Solving
X2 + -2xy + y2 = 1 + 6x + -4y

Solving for variable 'X'.

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

Add '2xy' to each side of the equation.
X2 + -2xy + 2xy + y2 = 1 + 6x + 2xy + -4y

Combine like terms: -2xy + 2xy = 0
X2 + 0 + y2 = 1 + 6x + 2xy + -4y
X2 + y2 = 1 + 6x + 2xy + -4y

Add '-1y2' to each side of the equation.
X2 + y2 + -1y2 = 1 + 6x + 2xy + -4y + -1y2

Combine like terms: y2 + -1y2 = 0
X2 + 0 = 1 + 6x + 2xy + -4y + -1y2
X2 = 1 + 6x + 2xy + -4y + -1y2

Simplifying
X2 = 1 + 6x + 2xy + -4y + -1y2

Reorder the terms:
-1 + X2 + -6x + -2xy + 4y + y2 = 1 + 6x + 2xy + -4y + -1y2 + -1 + -6x + -2xy + 4y + y2

Reorder the terms:
-1 + X2 + -6x + -2xy + 4y + y2 = 1 + -1 + 6x + -6x + 2xy + -2xy + -4y + 4y + -1y2 + y2

Combine like terms: 1 + -1 = 0
-1 + X2 + -6x + -2xy + 4y + y2 = 0 + 6x + -6x + 2xy + -2xy + -4y + 4y + -1y2 + y2
-1 + X2 + -6x + -2xy + 4y + y2 = 6x + -6x + 2xy + -2xy + -4y + 4y + -1y2 + y2

Combine like terms: 6x + -6x = 0
-1 + X2 + -6x + -2xy + 4y + y2 = 0 + 2xy + -2xy + -4y + 4y + -1y2 + y2
-1 + X2 + -6x + -2xy + 4y + y2 = 2xy + -2xy + -4y + 4y + -1y2 + y2

Combine like terms: 2xy + -2xy = 0
-1 + X2 + -6x + -2xy + 4y + y2 = 0 + -4y + 4y + -1y2 + y2
-1 + X2 + -6x + -2xy + 4y + y2 = -4y + 4y + -1y2 + y2

Combine like terms: -4y + 4y = 0
-1 + X2 + -6x + -2xy + 4y + y2 = 0 + -1y2 + y2
-1 + X2 + -6x + -2xy + 4y + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-1 + X2 + -6x + -2xy + 4y + y2 = 0

The solution to this equation could not be determined.

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