(1+k)x^2+(1+k)y^2-(k+9)x-2(5k-1)y+9k+5=0

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Solution for (1+k)x^2+(1+k)y^2-(k+9)x-2(5k-1)y+9k+5=0 equation: 


Simplifying
(1 + k) * x2 + (1 + k) * y2 + -1(k + 9) * x + -2(5k + -1) * y + 9k + 5 = 0

Reorder the terms for easier multiplication:
x2(1 + k) + (1 + k) * y2 + -1(k + 9) * x + -2(5k + -1) * y + 9k + 5 = 0
(1 * x2 + k * x2) + (1 + k) * y2 + -1(k + 9) * x + -2(5k + -1) * y + 9k + 5 = 0

Reorder the terms:
(kx2 + 1x2) + (1 + k) * y2 + -1(k + 9) * x + -2(5k + -1) * y + 9k + 5 = 0
(kx2 + 1x2) + (1 + k) * y2 + -1(k + 9) * x + -2(5k + -1) * y + 9k + 5 = 0

Reorder the terms for easier multiplication:
kx2 + 1x2 + y2(1 + k) + -1(k + 9) * x + -2(5k + -1) * y + 9k + 5 = 0
kx2 + 1x2 + (1 * y2 + k * y2) + -1(k + 9) * x + -2(5k + -1) * y + 9k + 5 = 0

Reorder the terms:
kx2 + 1x2 + (ky2 + 1y2) + -1(k + 9) * x + -2(5k + -1) * y + 9k + 5 = 0
kx2 + 1x2 + (ky2 + 1y2) + -1(k + 9) * x + -2(5k + -1) * y + 9k + 5 = 0

Reorder the terms:
kx2 + 1x2 + ky2 + 1y2 + -1(9 + k) * x + -2(5k + -1) * y + 9k + 5 = 0

Reorder the terms for easier multiplication:
kx2 + 1x2 + ky2 + 1y2 + -1x(9 + k) + -2(5k + -1) * y + 9k + 5 = 0
kx2 + 1x2 + ky2 + 1y2 + (9 * -1x + k * -1x) + -2(5k + -1) * y + 9k + 5 = 0

Reorder the terms:
kx2 + 1x2 + ky2 + 1y2 + (-1kx + -9x) + -2(5k + -1) * y + 9k + 5 = 0
kx2 + 1x2 + ky2 + 1y2 + (-1kx + -9x) + -2(5k + -1) * y + 9k + 5 = 0

Reorder the terms:
kx2 + 1x2 + ky2 + 1y2 + -1kx + -9x + -2(-1 + 5k) * y + 9k + 5 = 0

Reorder the terms for easier multiplication:
kx2 + 1x2 + ky2 + 1y2 + -1kx + -9x + -2y(-1 + 5k) + 9k + 5 = 0
kx2 + 1x2 + ky2 + 1y2 + -1kx + -9x + (-1 * -2y + 5k * -2y) + 9k + 5 = 0

Reorder the terms:
kx2 + 1x2 + ky2 + 1y2 + -1kx + -9x + (-10ky + 2y) + 9k + 5 = 0
kx2 + 1x2 + ky2 + 1y2 + -1kx + -9x + (-10ky + 2y) + 9k + 5 = 0

Reorder the terms:
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + 1x2 + 2y + 1y2 = 0

Solving
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + 1x2 + 2y + 1y2 = 0

Solving for variable 'k'.

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

Add '-5' to each side of the equation.
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + 1x2 + 2y + -5 + 1y2 = 0 + -5

Reorder the terms:
5 + -5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + 1x2 + 2y + 1y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + 1x2 + 2y + 1y2 = 0 + -5
9k + -1kx + kx2 + -10ky + ky2 + -9x + 1x2 + 2y + 1y2 = 0 + -5

Combine like terms: 0 + -5 = -5
9k + -1kx + kx2 + -10ky + ky2 + -9x + 1x2 + 2y + 1y2 = -5

Add '9x' to each side of the equation.
9k + -1kx + kx2 + -10ky + ky2 + -9x + 1x2 + 2y + 9x + 1y2 = -5 + 9x

Reorder the terms:
9k + -1kx + kx2 + -10ky + ky2 + -9x + 9x + 1x2 + 2y + 1y2 = -5 + 9x

Combine like terms: -9x + 9x = 0
9k + -1kx + kx2 + -10ky + ky2 + 0 + 1x2 + 2y + 1y2 = -5 + 9x
9k + -1kx + kx2 + -10ky + ky2 + 1x2 + 2y + 1y2 = -5 + 9x

Add '-1x2' to each side of the equation.
9k + -1kx + kx2 + -10ky + ky2 + 1x2 + 2y + -1x2 + 1y2 = -5 + 9x + -1x2

Reorder the terms:
9k + -1kx + kx2 + -10ky + ky2 + 1x2 + -1x2 + 2y + 1y2 = -5 + 9x + -1x2

Combine like terms: 1x2 + -1x2 = 0
9k + -1kx + kx2 + -10ky + ky2 + 0 + 2y + 1y2 = -5 + 9x + -1x2
9k + -1kx + kx2 + -10ky + ky2 + 2y + 1y2 = -5 + 9x + -1x2

Add '-2y' to each side of the equation.
9k + -1kx + kx2 + -10ky + ky2 + 2y + -2y + 1y2 = -5 + 9x + -1x2 + -2y

Combine like terms: 2y + -2y = 0
9k + -1kx + kx2 + -10ky + ky2 + 0 + 1y2 = -5 + 9x + -1x2 + -2y
9k + -1kx + kx2 + -10ky + ky2 + 1y2 = -5 + 9x + -1x2 + -2y

Add '-1y2' to each side of the equation.
9k + -1kx + kx2 + -10ky + ky2 + 1y2 + -1y2 = -5 + 9x + -1x2 + -2y + -1y2

Combine like terms: 1y2 + -1y2 = 0
9k + -1kx + kx2 + -10ky + ky2 + 0 = -5 + 9x + -1x2 + -2y + -1y2
9k + -1kx + kx2 + -10ky + ky2 = -5 + 9x + -1x2 + -2y + -1y2

Reorder the terms:
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + x2 + 2y + y2 = -5 + 9x + -1x2 + -2y + -1y2 + 5 + -9x + x2 + 2y + y2

Reorder the terms:
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + x2 + 2y + y2 = -5 + 5 + 9x + -9x + -1x2 + x2 + -2y + 2y + -1y2 + y2

Combine like terms: -5 + 5 = 0
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + x2 + 2y + y2 = 0 + 9x + -9x + -1x2 + x2 + -2y + 2y + -1y2 + y2
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + x2 + 2y + y2 = 9x + -9x + -1x2 + x2 + -2y + 2y + -1y2 + y2

Combine like terms: 9x + -9x = 0
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + x2 + 2y + y2 = 0 + -1x2 + x2 + -2y + 2y + -1y2 + y2
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + x2 + 2y + y2 = -1x2 + x2 + -2y + 2y + -1y2 + y2

Combine like terms: -1x2 + x2 = 0
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + x2 + 2y + y2 = 0 + -2y + 2y + -1y2 + y2
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + x2 + 2y + y2 = -2y + 2y + -1y2 + y2

Combine like terms: -2y + 2y = 0
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + x2 + 2y + y2 = 0 + -1y2 + y2
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + x2 + 2y + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
5 + 9k + -1kx + kx2 + -10ky + ky2 + -9x + x2 + 2y + y2 = 0

The solution to this equation could not be determined.

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