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Simplifying x2 + y2 + 8x + -2ky + 18 = 0 Reorder the terms: 18 + -2ky + 8x + x2 + y2 = 0 Solving 18 + -2ky + 8x + x2 + y2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -2ky + 8x + x2 + -18 + y2 = 0 + -18 Reorder the terms: 18 + -18 + -2ky + 8x + x2 + y2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -2ky + 8x + x2 + y2 = 0 + -18 -2ky + 8x + x2 + y2 = 0 + -18 Combine like terms: 0 + -18 = -18 -2ky + 8x + x2 + y2 = -18 Add '-8x' to each side of the equation. -2ky + 8x + x2 + -8x + y2 = -18 + -8x Reorder the terms: -2ky + 8x + -8x + x2 + y2 = -18 + -8x Combine like terms: 8x + -8x = 0 -2ky + 0 + x2 + y2 = -18 + -8x -2ky + x2 + y2 = -18 + -8x Add '-1x2' to each side of the equation. -2ky + x2 + -1x2 + y2 = -18 + -8x + -1x2 Combine like terms: x2 + -1x2 = 0 -2ky + 0 + y2 = -18 + -8x + -1x2 -2ky + y2 = -18 + -8x + -1x2 Add '-1y2' to each side of the equation. -2ky + y2 + -1y2 = -18 + -8x + -1x2 + -1y2 Combine like terms: y2 + -1y2 = 0 -2ky + 0 = -18 + -8x + -1x2 + -1y2 -2ky = -18 + -8x + -1x2 + -1y2 Divide each side by '-2y'. k = 9y-1 + 4xy-1 + 0.5x2y-1 + 0.5y Simplifying k = 9y-1 + 4xy-1 + 0.5x2y-1 + 0.5y Reorder the terms: k = 4xy-1 + 0.5x2y-1 + 9y-1 + 0.5y
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