(1+k)x^2+(1+k)y^2+2(1+k)x-4(1+k)y-1+2k=0

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Solution for (1+k)x^2+(1+k)y^2+2(1+k)x-4(1+k)y-1+2k=0 equation: 


Simplifying
(1 + k) * x2 + (1 + k) * y2 + 2(1 + k) * x + -4(1 + k) * y + -1 + 2k = 0

Reorder the terms for easier multiplication:
x2(1 + k) + (1 + k) * y2 + 2(1 + k) * x + -4(1 + k) * y + -1 + 2k = 0
(1 * x2 + k * x2) + (1 + k) * y2 + 2(1 + k) * x + -4(1 + k) * y + -1 + 2k = 0

Reorder the terms:
(kx2 + 1x2) + (1 + k) * y2 + 2(1 + k) * x + -4(1 + k) * y + -1 + 2k = 0
(kx2 + 1x2) + (1 + k) * y2 + 2(1 + k) * x + -4(1 + k) * y + -1 + 2k = 0

Reorder the terms for easier multiplication:
kx2 + 1x2 + y2(1 + k) + 2(1 + k) * x + -4(1 + k) * y + -1 + 2k = 0
kx2 + 1x2 + (1 * y2 + k * y2) + 2(1 + k) * x + -4(1 + k) * y + -1 + 2k = 0

Reorder the terms:
kx2 + 1x2 + (ky2 + 1y2) + 2(1 + k) * x + -4(1 + k) * y + -1 + 2k = 0
kx2 + 1x2 + (ky2 + 1y2) + 2(1 + k) * x + -4(1 + k) * y + -1 + 2k = 0

Reorder the terms for easier multiplication:
kx2 + 1x2 + ky2 + 1y2 + 2x(1 + k) + -4(1 + k) * y + -1 + 2k = 0
kx2 + 1x2 + ky2 + 1y2 + (1 * 2x + k * 2x) + -4(1 + k) * y + -1 + 2k = 0

Reorder the terms:
kx2 + 1x2 + ky2 + 1y2 + (2kx + 2x) + -4(1 + k) * y + -1 + 2k = 0
kx2 + 1x2 + ky2 + 1y2 + (2kx + 2x) + -4(1 + k) * y + -1 + 2k = 0

Reorder the terms for easier multiplication:
kx2 + 1x2 + ky2 + 1y2 + 2kx + 2x + -4y(1 + k) + -1 + 2k = 0
kx2 + 1x2 + ky2 + 1y2 + 2kx + 2x + (1 * -4y + k * -4y) + -1 + 2k = 0

Reorder the terms:
kx2 + 1x2 + ky2 + 1y2 + 2kx + 2x + (-4ky + -4y) + -1 + 2k = 0
kx2 + 1x2 + ky2 + 1y2 + 2kx + 2x + (-4ky + -4y) + -1 + 2k = 0

Reorder the terms:
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + 1x2 + -4y + 1y2 = 0

Solving
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + 1x2 + -4y + 1y2 = 0

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + 1x2 + -4y + 1 + 1y2 = 0 + 1

Reorder the terms:
-1 + 1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + 1x2 + -4y + 1y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + 1x2 + -4y + 1y2 = 0 + 1
2k + 2kx + kx2 + -4ky + ky2 + 2x + 1x2 + -4y + 1y2 = 0 + 1

Combine like terms: 0 + 1 = 1
2k + 2kx + kx2 + -4ky + ky2 + 2x + 1x2 + -4y + 1y2 = 1

Add '-2x' to each side of the equation.
2k + 2kx + kx2 + -4ky + ky2 + 2x + 1x2 + -4y + -2x + 1y2 = 1 + -2x

Reorder the terms:
2k + 2kx + kx2 + -4ky + ky2 + 2x + -2x + 1x2 + -4y + 1y2 = 1 + -2x

Combine like terms: 2x + -2x = 0
2k + 2kx + kx2 + -4ky + ky2 + 0 + 1x2 + -4y + 1y2 = 1 + -2x
2k + 2kx + kx2 + -4ky + ky2 + 1x2 + -4y + 1y2 = 1 + -2x

Add '-1x2' to each side of the equation.
2k + 2kx + kx2 + -4ky + ky2 + 1x2 + -4y + -1x2 + 1y2 = 1 + -2x + -1x2

Reorder the terms:
2k + 2kx + kx2 + -4ky + ky2 + 1x2 + -1x2 + -4y + 1y2 = 1 + -2x + -1x2

Combine like terms: 1x2 + -1x2 = 0
2k + 2kx + kx2 + -4ky + ky2 + 0 + -4y + 1y2 = 1 + -2x + -1x2
2k + 2kx + kx2 + -4ky + ky2 + -4y + 1y2 = 1 + -2x + -1x2

Add '4y' to each side of the equation.
2k + 2kx + kx2 + -4ky + ky2 + -4y + 4y + 1y2 = 1 + -2x + -1x2 + 4y

Combine like terms: -4y + 4y = 0
2k + 2kx + kx2 + -4ky + ky2 + 0 + 1y2 = 1 + -2x + -1x2 + 4y
2k + 2kx + kx2 + -4ky + ky2 + 1y2 = 1 + -2x + -1x2 + 4y

Add '-1y2' to each side of the equation.
2k + 2kx + kx2 + -4ky + ky2 + 1y2 + -1y2 = 1 + -2x + -1x2 + 4y + -1y2

Combine like terms: 1y2 + -1y2 = 0
2k + 2kx + kx2 + -4ky + ky2 + 0 = 1 + -2x + -1x2 + 4y + -1y2
2k + 2kx + kx2 + -4ky + ky2 = 1 + -2x + -1x2 + 4y + -1y2

Reorder the terms:
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + x2 + -4y + y2 = 1 + -2x + -1x2 + 4y + -1y2 + -1 + 2x + x2 + -4y + y2

Reorder the terms:
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + x2 + -4y + y2 = 1 + -1 + -2x + 2x + -1x2 + x2 + 4y + -4y + -1y2 + y2

Combine like terms: 1 + -1 = 0
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + x2 + -4y + y2 = 0 + -2x + 2x + -1x2 + x2 + 4y + -4y + -1y2 + y2
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + x2 + -4y + y2 = -2x + 2x + -1x2 + x2 + 4y + -4y + -1y2 + y2

Combine like terms: -2x + 2x = 0
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + x2 + -4y + y2 = 0 + -1x2 + x2 + 4y + -4y + -1y2 + y2
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + x2 + -4y + y2 = -1x2 + x2 + 4y + -4y + -1y2 + y2

Combine like terms: -1x2 + x2 = 0
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + x2 + -4y + y2 = 0 + 4y + -4y + -1y2 + y2
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + x2 + -4y + y2 = 4y + -4y + -1y2 + y2

Combine like terms: 4y + -4y = 0
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + x2 + -4y + y2 = 0 + -1y2 + y2
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + x2 + -4y + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-1 + 2k + 2kx + kx2 + -4ky + ky2 + 2x + x2 + -4y + y2 = 0

The solution to this equation could not be determined.

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