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Simplifying (x + 2y + 1) * dx + -1(3x + 6y + -1) * dy = 0 Reorder the terms: (1 + x + 2y) * dx + -1(3x + 6y + -1) * dy = 0 Reorder the terms for easier multiplication: dx(1 + x + 2y) + -1(3x + 6y + -1) * dy = 0 (1 * dx + x * dx + 2y * dx) + -1(3x + 6y + -1) * dy = 0 Reorder the terms: (1dx + 2dxy + dx2) + -1(3x + 6y + -1) * dy = 0 (1dx + 2dxy + dx2) + -1(3x + 6y + -1) * dy = 0 Reorder the terms: 1dx + 2dxy + dx2 + -1(-1 + 3x + 6y) * dy = 0 Reorder the terms for easier multiplication: 1dx + 2dxy + dx2 + -1dy(-1 + 3x + 6y) = 0 1dx + 2dxy + dx2 + (-1 * -1dy + 3x * -1dy + 6y * -1dy) = 0 Reorder the terms: 1dx + 2dxy + dx2 + (-3dxy + 1dy + -6dy2) = 0 1dx + 2dxy + dx2 + (-3dxy + 1dy + -6dy2) = 0 Reorder the terms: 1dx + 2dxy + -3dxy + dx2 + 1dy + -6dy2 = 0 Combine like terms: 2dxy + -3dxy = -1dxy 1dx + -1dxy + dx2 + 1dy + -6dy2 = 0 Solving 1dx + -1dxy + dx2 + 1dy + -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(x + -1xy + x2 + y + -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 '(x + -1xy + x2 + y + -6y2)' equal to zero and attempt to solve: Simplifying x + -1xy + x2 + y + -6y2 = 0 Solving x + -1xy + x2 + y + -6y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1xy + x2 + y + -1x + -6y2 = 0 + -1x Reorder the terms: x + -1x + -1xy + x2 + y + -6y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + -1xy + x2 + y + -6y2 = 0 + -1x -1xy + x2 + y + -6y2 = 0 + -1x Remove the zero: -1xy + x2 + y + -6y2 = -1x Add 'xy' to each side of the equation. -1xy + x2 + y + xy + -6y2 = -1x + xy Reorder the terms: -1xy + xy + x2 + y + -6y2 = -1x + xy Combine like terms: -1xy + xy = 0 0 + x2 + y + -6y2 = -1x + xy x2 + y + -6y2 = -1x + xy Add '-1x2' to each side of the equation. x2 + y + -1x2 + -6y2 = -1x + xy + -1x2 Reorder the terms: x2 + -1x2 + y + -6y2 = -1x + xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + y + -6y2 = -1x + xy + -1x2 y + -6y2 = -1x + xy + -1x2 Add '-1y' to each side of the equation. y + -1y + -6y2 = -1x + xy + -1x2 + -1y Combine like terms: y + -1y = 0 0 + -6y2 = -1x + xy + -1x2 + -1y -6y2 = -1x + xy + -1x2 + -1y Add '6y2' to each side of the equation. -6y2 + 6y2 = -1x + xy + -1x2 + -1y + 6y2 Combine like terms: -6y2 + 6y2 = 0 0 = -1x + xy + -1x2 + -1y + 6y2 Simplifying 0 = -1x + xy + -1x2 + -1y + 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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