5x^2+2Y^2+2xy-2x-4y+2=0

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Solution for 5x^2+2Y^2+2xy-2x-4y+2=0 equation: 


Simplifying
5x2 + 2Y2 + 2xy + -2x + -4y + 2 = 0

Reorder the terms:
2 + 2Y2 + -2x + 2xy + 5x2 + -4y = 0

Solving
2 + 2Y2 + -2x + 2xy + 5x2 + -4y = 0

Solving for variable 'Y'.

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

Add '-2' to each side of the equation.
2 + 2Y2 + -2x + 2xy + 5x2 + -2 + -4y = 0 + -2

Reorder the terms:
2 + -2 + 2Y2 + -2x + 2xy + 5x2 + -4y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2Y2 + -2x + 2xy + 5x2 + -4y = 0 + -2
2Y2 + -2x + 2xy + 5x2 + -4y = 0 + -2

Combine like terms: 0 + -2 = -2
2Y2 + -2x + 2xy + 5x2 + -4y = -2

Add '2x' to each side of the equation.
2Y2 + -2x + 2xy + 5x2 + 2x + -4y = -2 + 2x

Reorder the terms:
2Y2 + -2x + 2x + 2xy + 5x2 + -4y = -2 + 2x

Combine like terms: -2x + 2x = 0
2Y2 + 0 + 2xy + 5x2 + -4y = -2 + 2x
2Y2 + 2xy + 5x2 + -4y = -2 + 2x

Add '-2xy' to each side of the equation.
2Y2 + 2xy + 5x2 + -2xy + -4y = -2 + 2x + -2xy

Reorder the terms:
2Y2 + 2xy + -2xy + 5x2 + -4y = -2 + 2x + -2xy

Combine like terms: 2xy + -2xy = 0
2Y2 + 0 + 5x2 + -4y = -2 + 2x + -2xy
2Y2 + 5x2 + -4y = -2 + 2x + -2xy

Add '-5x2' to each side of the equation.
2Y2 + 5x2 + -5x2 + -4y = -2 + 2x + -2xy + -5x2

Combine like terms: 5x2 + -5x2 = 0
2Y2 + 0 + -4y = -2 + 2x + -2xy + -5x2
2Y2 + -4y = -2 + 2x + -2xy + -5x2

Add '4y' to each side of the equation.
2Y2 + -4y + 4y = -2 + 2x + -2xy + -5x2 + 4y

Combine like terms: -4y + 4y = 0
2Y2 + 0 = -2 + 2x + -2xy + -5x2 + 4y
2Y2 = -2 + 2x + -2xy + -5x2 + 4y

Divide each side by '2'.
Y2 = -1 + x + -1xy + -2.5x2 + 2y

Simplifying
Y2 = -1 + x + -1xy + -2.5x2 + 2y

Reorder the terms:
1 + Y2 + -1x + xy + 2.5x2 + -2y = -1 + x + -1xy + -2.5x2 + 2y + 1 + -1x + xy + 2.5x2 + -2y

Reorder the terms:
1 + Y2 + -1x + xy + 2.5x2 + -2y = -1 + 1 + x + -1x + -1xy + xy + -2.5x2 + 2.5x2 + 2y + -2y

Combine like terms: -1 + 1 = 0
1 + Y2 + -1x + xy + 2.5x2 + -2y = 0 + x + -1x + -1xy + xy + -2.5x2 + 2.5x2 + 2y + -2y
1 + Y2 + -1x + xy + 2.5x2 + -2y = x + -1x + -1xy + xy + -2.5x2 + 2.5x2 + 2y + -2y

Combine like terms: x + -1x = 0
1 + Y2 + -1x + xy + 2.5x2 + -2y = 0 + -1xy + xy + -2.5x2 + 2.5x2 + 2y + -2y
1 + Y2 + -1x + xy + 2.5x2 + -2y = -1xy + xy + -2.5x2 + 2.5x2 + 2y + -2y

Combine like terms: -1xy + xy = 0
1 + Y2 + -1x + xy + 2.5x2 + -2y = 0 + -2.5x2 + 2.5x2 + 2y + -2y
1 + Y2 + -1x + xy + 2.5x2 + -2y = -2.5x2 + 2.5x2 + 2y + -2y

Combine like terms: -2.5x2 + 2.5x2 = 0.0
1 + Y2 + -1x + xy + 2.5x2 + -2y = 0.0 + 2y + -2y
1 + Y2 + -1x + xy + 2.5x2 + -2y = 2y + -2y

Combine like terms: 2y + -2y = 0
1 + Y2 + -1x + xy + 2.5x2 + -2y = 0

The solution to this equation could not be determined.

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