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Simplifying (1 + k) * x2 + (1 + k) * y2 + 2(1 + -4k) * y + 2 + k = 0 Reorder the terms for easier multiplication: x2(1 + k) + (1 + k) * y2 + 2(1 + -4k) * y + 2 + k = 0 (1 * x2 + k * x2) + (1 + k) * y2 + 2(1 + -4k) * y + 2 + k = 0 Reorder the terms: (kx2 + 1x2) + (1 + k) * y2 + 2(1 + -4k) * y + 2 + k = 0 (kx2 + 1x2) + (1 + k) * y2 + 2(1 + -4k) * y + 2 + k = 0 Reorder the terms for easier multiplication: kx2 + 1x2 + y2(1 + k) + 2(1 + -4k) * y + 2 + k = 0 kx2 + 1x2 + (1 * y2 + k * y2) + 2(1 + -4k) * y + 2 + k = 0 Reorder the terms: kx2 + 1x2 + (ky2 + 1y2) + 2(1 + -4k) * y + 2 + k = 0 kx2 + 1x2 + (ky2 + 1y2) + 2(1 + -4k) * y + 2 + k = 0 Reorder the terms for easier multiplication: kx2 + 1x2 + ky2 + 1y2 + 2y(1 + -4k) + 2 + k = 0 kx2 + 1x2 + ky2 + 1y2 + (1 * 2y + -4k * 2y) + 2 + k = 0 Reorder the terms: kx2 + 1x2 + ky2 + 1y2 + (-8ky + 2y) + 2 + k = 0 kx2 + 1x2 + ky2 + 1y2 + (-8ky + 2y) + 2 + k = 0 Reorder the terms: 2 + k + kx2 + -8ky + ky2 + 1x2 + 2y + 1y2 = 0 Solving 2 + k + kx2 + -8ky + ky2 + 1x2 + 2y + 1y2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + k + kx2 + -8ky + ky2 + 1x2 + 2y + -2 + 1y2 = 0 + -2 Reorder the terms: 2 + -2 + k + kx2 + -8ky + ky2 + 1x2 + 2y + 1y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + k + kx2 + -8ky + ky2 + 1x2 + 2y + 1y2 = 0 + -2 k + kx2 + -8ky + ky2 + 1x2 + 2y + 1y2 = 0 + -2 Combine like terms: 0 + -2 = -2 k + kx2 + -8ky + ky2 + 1x2 + 2y + 1y2 = -2 Add '-1x2' to each side of the equation. k + kx2 + -8ky + ky2 + 1x2 + 2y + -1x2 + 1y2 = -2 + -1x2 Reorder the terms: k + kx2 + -8ky + ky2 + 1x2 + -1x2 + 2y + 1y2 = -2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 k + kx2 + -8ky + ky2 + 0 + 2y + 1y2 = -2 + -1x2 k + kx2 + -8ky + ky2 + 2y + 1y2 = -2 + -1x2 Add '-2y' to each side of the equation. k + kx2 + -8ky + ky2 + 2y + -2y + 1y2 = -2 + -1x2 + -2y Combine like terms: 2y + -2y = 0 k + kx2 + -8ky + ky2 + 0 + 1y2 = -2 + -1x2 + -2y k + kx2 + -8ky + ky2 + 1y2 = -2 + -1x2 + -2y Add '-1y2' to each side of the equation. k + kx2 + -8ky + ky2 + 1y2 + -1y2 = -2 + -1x2 + -2y + -1y2 Combine like terms: 1y2 + -1y2 = 0 k + kx2 + -8ky + ky2 + 0 = -2 + -1x2 + -2y + -1y2 k + kx2 + -8ky + ky2 = -2 + -1x2 + -2y + -1y2 Reorder the terms: 2 + k + kx2 + -8ky + ky2 + x2 + 2y + y2 = -2 + -1x2 + -2y + -1y2 + 2 + x2 + 2y + y2 Reorder the terms: 2 + k + kx2 + -8ky + ky2 + x2 + 2y + y2 = -2 + 2 + -1x2 + x2 + -2y + 2y + -1y2 + y2 Combine like terms: -2 + 2 = 0 2 + k + kx2 + -8ky + ky2 + x2 + 2y + y2 = 0 + -1x2 + x2 + -2y + 2y + -1y2 + y2 2 + k + kx2 + -8ky + ky2 + x2 + 2y + y2 = -1x2 + x2 + -2y + 2y + -1y2 + y2 Combine like terms: -1x2 + x2 = 0 2 + k + kx2 + -8ky + ky2 + x2 + 2y + y2 = 0 + -2y + 2y + -1y2 + y2 2 + k + kx2 + -8ky + ky2 + x2 + 2y + y2 = -2y + 2y + -1y2 + y2 Combine like terms: -2y + 2y = 0 2 + k + kx2 + -8ky + ky2 + x2 + 2y + y2 = 0 + -1y2 + y2 2 + k + kx2 + -8ky + ky2 + x2 + 2y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 2 + k + kx2 + -8ky + ky2 + x2 + 2y + y2 = 0 The solution to this equation could not be determined.
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