x^2+y^2+2ax+2by+c=0

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Solution for x^2+y^2+2ax+2by+c=0 equation:


Simplifying
x2 + y2 + 2ax + 2by + c = 0

Reorder the terms:
2ax + 2by + c + x2 + y2 = 0

Solving
2ax + 2by + c + x2 + y2 = 0

Solving for variable 'a'.

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

Add '-2by' to each side of the equation.
2ax + 2by + c + x2 + -2by + y2 = 0 + -2by

Reorder the terms:
2ax + 2by + -2by + c + x2 + y2 = 0 + -2by

Combine like terms: 2by + -2by = 0
2ax + 0 + c + x2 + y2 = 0 + -2by
2ax + c + x2 + y2 = 0 + -2by
Remove the zero:
2ax + c + x2 + y2 = -2by

Add '-1c' to each side of the equation.
2ax + c + x2 + -1c + y2 = -2by + -1c

Reorder the terms:
2ax + c + -1c + x2 + y2 = -2by + -1c

Combine like terms: c + -1c = 0
2ax + 0 + x2 + y2 = -2by + -1c
2ax + x2 + y2 = -2by + -1c

Add '-1x2' to each side of the equation.
2ax + x2 + -1x2 + y2 = -2by + -1c + -1x2

Combine like terms: x2 + -1x2 = 0
2ax + 0 + y2 = -2by + -1c + -1x2
2ax + y2 = -2by + -1c + -1x2

Add '-1y2' to each side of the equation.
2ax + y2 + -1y2 = -2by + -1c + -1x2 + -1y2

Combine like terms: y2 + -1y2 = 0
2ax + 0 = -2by + -1c + -1x2 + -1y2
2ax = -2by + -1c + -1x2 + -1y2

Divide each side by '2x'.
a = -1bx-1y + -0.5cx-1 + -0.5x + -0.5x-1y2

Simplifying
a = -1bx-1y + -0.5cx-1 + -0.5x + -0.5x-1y2

Reorder the terms:
a = -1bx-1y + -0.5cx-1 + -0.5x-1y2 + -0.5x

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