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Simplifying (x + 2y + 8) * dx + -1(3x + -6y + 18) * dy = 0 Reorder the terms: (8 + x + 2y) * dx + -1(3x + -6y + 18) * dy = 0 Reorder the terms for easier multiplication: dx(8 + x + 2y) + -1(3x + -6y + 18) * dy = 0 (8 * dx + x * dx + 2y * dx) + -1(3x + -6y + 18) * dy = 0 Reorder the terms: (8dx + 2dxy + dx2) + -1(3x + -6y + 18) * dy = 0 (8dx + 2dxy + dx2) + -1(3x + -6y + 18) * dy = 0 Reorder the terms: 8dx + 2dxy + dx2 + -1(18 + 3x + -6y) * dy = 0 Reorder the terms for easier multiplication: 8dx + 2dxy + dx2 + -1dy(18 + 3x + -6y) = 0 8dx + 2dxy + dx2 + (18 * -1dy + 3x * -1dy + -6y * -1dy) = 0 Reorder the terms: 8dx + 2dxy + dx2 + (-3dxy + -18dy + 6dy2) = 0 8dx + 2dxy + dx2 + (-3dxy + -18dy + 6dy2) = 0 Reorder the terms: 8dx + 2dxy + -3dxy + dx2 + -18dy + 6dy2 = 0 Combine like terms: 2dxy + -3dxy = -1dxy 8dx + -1dxy + dx2 + -18dy + 6dy2 = 0 Solving 8dx + -1dxy + dx2 + -18dy + 6dy2 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'd'. d(8x + -1xy + x2 + -18y + 6y2) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(8x + -1xy + x2 + -18y + 6y2)' equal to zero and attempt to solve: Simplifying 8x + -1xy + x2 + -18y + 6y2 = 0 Solving 8x + -1xy + x2 + -18y + 6y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-8x' to each side of the equation. 8x + -1xy + x2 + -18y + -8x + 6y2 = 0 + -8x Reorder the terms: 8x + -8x + -1xy + x2 + -18y + 6y2 = 0 + -8x Combine like terms: 8x + -8x = 0 0 + -1xy + x2 + -18y + 6y2 = 0 + -8x -1xy + x2 + -18y + 6y2 = 0 + -8x Remove the zero: -1xy + x2 + -18y + 6y2 = -8x Add 'xy' to each side of the equation. -1xy + x2 + -18y + xy + 6y2 = -8x + xy Reorder the terms: -1xy + xy + x2 + -18y + 6y2 = -8x + xy Combine like terms: -1xy + xy = 0 0 + x2 + -18y + 6y2 = -8x + xy x2 + -18y + 6y2 = -8x + xy Add '-1x2' to each side of the equation. x2 + -18y + -1x2 + 6y2 = -8x + xy + -1x2 Reorder the terms: x2 + -1x2 + -18y + 6y2 = -8x + xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -18y + 6y2 = -8x + xy + -1x2 -18y + 6y2 = -8x + xy + -1x2 Add '18y' to each side of the equation. -18y + 18y + 6y2 = -8x + xy + -1x2 + 18y Combine like terms: -18y + 18y = 0 0 + 6y2 = -8x + xy + -1x2 + 18y 6y2 = -8x + xy + -1x2 + 18y Add '-6y2' to each side of the equation. 6y2 + -6y2 = -8x + xy + -1x2 + 18y + -6y2 Combine like terms: 6y2 + -6y2 = 0 0 = -8x + xy + -1x2 + 18y + -6y2 Simplifying 0 = -8x + xy + -1x2 + 18y + -6y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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