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Simplifying (x + 2y + 1) * dx + (3x + 6y + 2) * dy = 0 Reorder the terms: (1 + x + 2y) * dx + (3x + 6y + 2) * dy = 0 Reorder the terms for easier multiplication: dx(1 + x + 2y) + (3x + 6y + 2) * dy = 0 (1 * dx + x * dx + 2y * dx) + (3x + 6y + 2) * dy = 0 Reorder the terms: (1dx + 2dxy + dx2) + (3x + 6y + 2) * dy = 0 (1dx + 2dxy + dx2) + (3x + 6y + 2) * dy = 0 Reorder the terms: 1dx + 2dxy + dx2 + (2 + 3x + 6y) * dy = 0 Reorder the terms for easier multiplication: 1dx + 2dxy + dx2 + dy(2 + 3x + 6y) = 0 1dx + 2dxy + dx2 + (2 * dy + 3x * dy + 6y * dy) = 0 Reorder the terms: 1dx + 2dxy + dx2 + (3dxy + 2dy + 6dy2) = 0 1dx + 2dxy + dx2 + (3dxy + 2dy + 6dy2) = 0 Reorder the terms: 1dx + 2dxy + 3dxy + dx2 + 2dy + 6dy2 = 0 Combine like terms: 2dxy + 3dxy = 5dxy 1dx + 5dxy + dx2 + 2dy + 6dy2 = 0 Solving 1dx + 5dxy + dx2 + 2dy + 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 + 5xy + x2 + 2y + 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 + 5xy + x2 + 2y + 6y2)' equal to zero and attempt to solve: Simplifying x + 5xy + x2 + 2y + 6y2 = 0 Solving x + 5xy + x2 + 2y + 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 + 5xy + x2 + 2y + -1x + 6y2 = 0 + -1x Reorder the terms: x + -1x + 5xy + x2 + 2y + 6y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + 5xy + x2 + 2y + 6y2 = 0 + -1x 5xy + x2 + 2y + 6y2 = 0 + -1x Remove the zero: 5xy + x2 + 2y + 6y2 = -1x Add '-5xy' to each side of the equation. 5xy + x2 + 2y + -5xy + 6y2 = -1x + -5xy Reorder the terms: 5xy + -5xy + x2 + 2y + 6y2 = -1x + -5xy Combine like terms: 5xy + -5xy = 0 0 + x2 + 2y + 6y2 = -1x + -5xy x2 + 2y + 6y2 = -1x + -5xy Add '-1x2' to each side of the equation. x2 + 2y + -1x2 + 6y2 = -1x + -5xy + -1x2 Reorder the terms: x2 + -1x2 + 2y + 6y2 = -1x + -5xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2y + 6y2 = -1x + -5xy + -1x2 2y + 6y2 = -1x + -5xy + -1x2 Add '-2y' to each side of the equation. 2y + -2y + 6y2 = -1x + -5xy + -1x2 + -2y Combine like terms: 2y + -2y = 0 0 + 6y2 = -1x + -5xy + -1x2 + -2y 6y2 = -1x + -5xy + -1x2 + -2y Add '-6y2' to each side of the equation. 6y2 + -6y2 = -1x + -5xy + -1x2 + -2y + -6y2 Combine like terms: 6y2 + -6y2 = 0 0 = -1x + -5xy + -1x2 + -2y + -6y2 Simplifying 0 = -1x + -5xy + -1x2 + -2y + -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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