x^2-2x+y^2+4Y=-1

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Solution for x^2-2x+y^2+4Y=-1 equation: 


Simplifying
x2 + -2x + y2 + 4Y = -1

Reorder the terms:
4Y + -2x + x2 + y2 = -1

Solving
4Y + -2x + x2 + y2 = -1

Solving for variable 'Y'.

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

Add '2x' to each side of the equation.
4Y + -2x + x2 + 2x + y2 = -1 + 2x

Reorder the terms:
4Y + -2x + 2x + x2 + y2 = -1 + 2x

Combine like terms: -2x + 2x = 0
4Y + 0 + x2 + y2 = -1 + 2x
4Y + x2 + y2 = -1 + 2x

Add '-1x2' to each side of the equation.
4Y + x2 + -1x2 + y2 = -1 + 2x + -1x2

Combine like terms: x2 + -1x2 = 0
4Y + 0 + y2 = -1 + 2x + -1x2
4Y + y2 = -1 + 2x + -1x2

Add '-1y2' to each side of the equation.
4Y + y2 + -1y2 = -1 + 2x + -1x2 + -1y2

Combine like terms: y2 + -1y2 = 0
4Y + 0 = -1 + 2x + -1x2 + -1y2
4Y = -1 + 2x + -1x2 + -1y2

Divide each side by '4'.
Y = -0.25 + 0.5x + -0.25x2 + -0.25y2

Simplifying
Y = -0.25 + 0.5x + -0.25x2 + -0.25y2

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