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Simplifying (x + -2y + -1) * dx + -1(2x + -4y + 3) * dy = 0 Reorder the terms: (-1 + x + -2y) * dx + -1(2x + -4y + 3) * dy = 0 Reorder the terms for easier multiplication: dx(-1 + x + -2y) + -1(2x + -4y + 3) * dy = 0 (-1 * dx + x * dx + -2y * dx) + -1(2x + -4y + 3) * dy = 0 Reorder the terms: (-1dx + -2dxy + dx2) + -1(2x + -4y + 3) * dy = 0 (-1dx + -2dxy + dx2) + -1(2x + -4y + 3) * dy = 0 Reorder the terms: -1dx + -2dxy + dx2 + -1(3 + 2x + -4y) * dy = 0 Reorder the terms for easier multiplication: -1dx + -2dxy + dx2 + -1dy(3 + 2x + -4y) = 0 -1dx + -2dxy + dx2 + (3 * -1dy + 2x * -1dy + -4y * -1dy) = 0 Reorder the terms: -1dx + -2dxy + dx2 + (-2dxy + -3dy + 4dy2) = 0 -1dx + -2dxy + dx2 + (-2dxy + -3dy + 4dy2) = 0 Reorder the terms: -1dx + -2dxy + -2dxy + dx2 + -3dy + 4dy2 = 0 Combine like terms: -2dxy + -2dxy = -4dxy -1dx + -4dxy + dx2 + -3dy + 4dy2 = 0 Solving -1dx + -4dxy + dx2 + -3dy + 4dy2 = 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(-1x + -4xy + x2 + -3y + 4y2) = 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 '(-1x + -4xy + x2 + -3y + 4y2)' equal to zero and attempt to solve: Simplifying -1x + -4xy + x2 + -3y + 4y2 = 0 Solving -1x + -4xy + x2 + -3y + 4y2 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + -4xy + x2 + -3y + x + 4y2 = 0 + x Reorder the terms: -1x + x + -4xy + x2 + -3y + 4y2 = 0 + x Combine like terms: -1x + x = 0 0 + -4xy + x2 + -3y + 4y2 = 0 + x -4xy + x2 + -3y + 4y2 = 0 + x Remove the zero: -4xy + x2 + -3y + 4y2 = x Add '4xy' to each side of the equation. -4xy + x2 + -3y + 4xy + 4y2 = x + 4xy Reorder the terms: -4xy + 4xy + x2 + -3y + 4y2 = x + 4xy Combine like terms: -4xy + 4xy = 0 0 + x2 + -3y + 4y2 = x + 4xy x2 + -3y + 4y2 = x + 4xy Add '-1x2' to each side of the equation. x2 + -3y + -1x2 + 4y2 = x + 4xy + -1x2 Reorder the terms: x2 + -1x2 + -3y + 4y2 = x + 4xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -3y + 4y2 = x + 4xy + -1x2 -3y + 4y2 = x + 4xy + -1x2 Add '3y' to each side of the equation. -3y + 3y + 4y2 = x + 4xy + -1x2 + 3y Combine like terms: -3y + 3y = 0 0 + 4y2 = x + 4xy + -1x2 + 3y 4y2 = x + 4xy + -1x2 + 3y Add '-4y2' to each side of the equation. 4y2 + -4y2 = x + 4xy + -1x2 + 3y + -4y2 Combine like terms: 4y2 + -4y2 = 0 0 = x + 4xy + -1x2 + 3y + -4y2 Simplifying 0 = x + 4xy + -1x2 + 3y + -4y2 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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