x^2-kx+y^2+2y=0

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Solution for x^2-kx+y^2+2y=0 equation:


Simplifying
x2 + -1kx + y2 + 2y = 0

Reorder the terms:
-1kx + x2 + 2y + y2 = 0

Solving
-1kx + x2 + 2y + y2 = 0

Solving for variable 'k'.

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

Add '-1x2' to each side of the equation.
-1kx + x2 + 2y + -1x2 + y2 = 0 + -1x2

Reorder the terms:
-1kx + x2 + -1x2 + 2y + y2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
-1kx + 0 + 2y + y2 = 0 + -1x2
-1kx + 2y + y2 = 0 + -1x2
Remove the zero:
-1kx + 2y + y2 = -1x2

Add '-2y' to each side of the equation.
-1kx + 2y + -2y + y2 = -1x2 + -2y

Combine like terms: 2y + -2y = 0
-1kx + 0 + y2 = -1x2 + -2y
-1kx + y2 = -1x2 + -2y

Add '-1y2' to each side of the equation.
-1kx + y2 + -1y2 = -1x2 + -2y + -1y2

Combine like terms: y2 + -1y2 = 0
-1kx + 0 = -1x2 + -2y + -1y2
-1kx = -1x2 + -2y + -1y2

Divide each side by '-1x'.
k = x + 2x-1y + x-1y2

Simplifying
k = x + 2x-1y + x-1y2

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

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