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Simplifying (1 + k) * x2 + (1 + k) * y2 + 2(1 + -4k) * x + -2y + 15k = 0 Reorder the terms for easier multiplication: x2(1 + k) + (1 + k) * y2 + 2(1 + -4k) * x + -2y + 15k = 0 (1 * x2 + k * x2) + (1 + k) * y2 + 2(1 + -4k) * x + -2y + 15k = 0 Reorder the terms: (kx2 + 1x2) + (1 + k) * y2 + 2(1 + -4k) * x + -2y + 15k = 0 (kx2 + 1x2) + (1 + k) * y2 + 2(1 + -4k) * x + -2y + 15k = 0 Reorder the terms for easier multiplication: kx2 + 1x2 + y2(1 + k) + 2(1 + -4k) * x + -2y + 15k = 0 kx2 + 1x2 + (1 * y2 + k * y2) + 2(1 + -4k) * x + -2y + 15k = 0 Reorder the terms: kx2 + 1x2 + (ky2 + 1y2) + 2(1 + -4k) * x + -2y + 15k = 0 kx2 + 1x2 + (ky2 + 1y2) + 2(1 + -4k) * x + -2y + 15k = 0 Reorder the terms for easier multiplication: kx2 + 1x2 + ky2 + 1y2 + 2x(1 + -4k) + -2y + 15k = 0 kx2 + 1x2 + ky2 + 1y2 + (1 * 2x + -4k * 2x) + -2y + 15k = 0 Reorder the terms: kx2 + 1x2 + ky2 + 1y2 + (-8kx + 2x) + -2y + 15k = 0 kx2 + 1x2 + ky2 + 1y2 + (-8kx + 2x) + -2y + 15k = 0 Reorder the terms: 15k + -8kx + kx2 + ky2 + 2x + 1x2 + -2y + 1y2 = 0 Solving 15k + -8kx + kx2 + ky2 + 2x + 1x2 + -2y + 1y2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2x' to each side of the equation. 15k + -8kx + kx2 + ky2 + 2x + 1x2 + -2y + -2x + 1y2 = 0 + -2x Reorder the terms: 15k + -8kx + kx2 + ky2 + 2x + -2x + 1x2 + -2y + 1y2 = 0 + -2x Combine like terms: 2x + -2x = 0 15k + -8kx + kx2 + ky2 + 0 + 1x2 + -2y + 1y2 = 0 + -2x 15k + -8kx + kx2 + ky2 + 1x2 + -2y + 1y2 = 0 + -2x Remove the zero: 15k + -8kx + kx2 + ky2 + 1x2 + -2y + 1y2 = -2x Add '-1x2' to each side of the equation. 15k + -8kx + kx2 + ky2 + 1x2 + -2y + -1x2 + 1y2 = -2x + -1x2 Reorder the terms: 15k + -8kx + kx2 + ky2 + 1x2 + -1x2 + -2y + 1y2 = -2x + -1x2 Combine like terms: 1x2 + -1x2 = 0 15k + -8kx + kx2 + ky2 + 0 + -2y + 1y2 = -2x + -1x2 15k + -8kx + kx2 + ky2 + -2y + 1y2 = -2x + -1x2 Add '2y' to each side of the equation. 15k + -8kx + kx2 + ky2 + -2y + 2y + 1y2 = -2x + -1x2 + 2y Combine like terms: -2y + 2y = 0 15k + -8kx + kx2 + ky2 + 0 + 1y2 = -2x + -1x2 + 2y 15k + -8kx + kx2 + ky2 + 1y2 = -2x + -1x2 + 2y Add '-1y2' to each side of the equation. 15k + -8kx + kx2 + ky2 + 1y2 + -1y2 = -2x + -1x2 + 2y + -1y2 Combine like terms: 1y2 + -1y2 = 0 15k + -8kx + kx2 + ky2 + 0 = -2x + -1x2 + 2y + -1y2 15k + -8kx + kx2 + ky2 = -2x + -1x2 + 2y + -1y2 Reorder the terms: 15k + -8kx + kx2 + ky2 + 2x + x2 + -2y + y2 = -2x + 2x + -1x2 + x2 + 2y + -2y + -1y2 + y2 Combine like terms: -2x + 2x = 0 15k + -8kx + kx2 + ky2 + 2x + x2 + -2y + y2 = 0 + -1x2 + x2 + 2y + -2y + -1y2 + y2 15k + -8kx + kx2 + ky2 + 2x + x2 + -2y + y2 = -1x2 + x2 + 2y + -2y + -1y2 + y2 Combine like terms: -1x2 + x2 = 0 15k + -8kx + kx2 + ky2 + 2x + x2 + -2y + y2 = 0 + 2y + -2y + -1y2 + y2 15k + -8kx + kx2 + ky2 + 2x + x2 + -2y + y2 = 2y + -2y + -1y2 + y2 Combine like terms: 2y + -2y = 0 15k + -8kx + kx2 + ky2 + 2x + x2 + -2y + y2 = 0 + -1y2 + y2 15k + -8kx + kx2 + ky2 + 2x + x2 + -2y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 15k + -8kx + kx2 + ky2 + 2x + x2 + -2y + y2 = 0 The solution to this equation could not be determined.
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