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Simplifying x2 + y2 + kx + 2y + 3 = 0 Reorder the terms: 3 + kx + x2 + 2y + y2 = 0 Solving 3 + kx + x2 + 2y + y2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + kx + x2 + 2y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + kx + x2 + 2y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + kx + x2 + 2y + y2 = 0 + -3 kx + x2 + 2y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 kx + x2 + 2y + y2 = -3 Add '-1x2' to each side of the equation. kx + x2 + 2y + -1x2 + y2 = -3 + -1x2 Reorder the terms: kx + x2 + -1x2 + 2y + y2 = -3 + -1x2 Combine like terms: x2 + -1x2 = 0 kx + 0 + 2y + y2 = -3 + -1x2 kx + 2y + y2 = -3 + -1x2 Add '-2y' to each side of the equation. kx + 2y + -2y + y2 = -3 + -1x2 + -2y Combine like terms: 2y + -2y = 0 kx + 0 + y2 = -3 + -1x2 + -2y kx + y2 = -3 + -1x2 + -2y Add '-1y2' to each side of the equation. kx + y2 + -1y2 = -3 + -1x2 + -2y + -1y2 Combine like terms: y2 + -1y2 = 0 kx + 0 = -3 + -1x2 + -2y + -1y2 kx = -3 + -1x2 + -2y + -1y2 Divide each side by 'x'. k = -3x-1 + -1x + -2x-1y + -1x-1y2 Simplifying k = -3x-1 + -1x + -2x-1y + -1x-1y2 Reorder the terms: k = -3x-1 + -2x-1y + -1x-1y2 + -1x
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