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Simplifying (x + 3y + -4) * dx + (x + 4y + -5) * dy = 0 Reorder the terms: (-4 + x + 3y) * dx + (x + 4y + -5) * dy = 0 Reorder the terms for easier multiplication: dx(-4 + x + 3y) + (x + 4y + -5) * dy = 0 (-4 * dx + x * dx + 3y * dx) + (x + 4y + -5) * dy = 0 Reorder the terms: (-4dx + 3dxy + dx2) + (x + 4y + -5) * dy = 0 (-4dx + 3dxy + dx2) + (x + 4y + -5) * dy = 0 Reorder the terms: -4dx + 3dxy + dx2 + (-5 + x + 4y) * dy = 0 Reorder the terms for easier multiplication: -4dx + 3dxy + dx2 + dy(-5 + x + 4y) = 0 -4dx + 3dxy + dx2 + (-5 * dy + x * dy + 4y * dy) = 0 Reorder the terms: -4dx + 3dxy + dx2 + (dxy + -5dy + 4dy2) = 0 -4dx + 3dxy + dx2 + (dxy + -5dy + 4dy2) = 0 Reorder the terms: -4dx + 3dxy + dxy + dx2 + -5dy + 4dy2 = 0 Combine like terms: 3dxy + dxy = 4dxy -4dx + 4dxy + dx2 + -5dy + 4dy2 = 0 Solving -4dx + 4dxy + dx2 + -5dy + 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(-4x + 4xy + x2 + -5y + 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 '(-4x + 4xy + x2 + -5y + 4y2)' equal to zero and attempt to solve: Simplifying -4x + 4xy + x2 + -5y + 4y2 = 0 Solving -4x + 4xy + x2 + -5y + 4y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '4x' to each side of the equation. -4x + 4xy + x2 + -5y + 4x + 4y2 = 0 + 4x Reorder the terms: -4x + 4x + 4xy + x2 + -5y + 4y2 = 0 + 4x Combine like terms: -4x + 4x = 0 0 + 4xy + x2 + -5y + 4y2 = 0 + 4x 4xy + x2 + -5y + 4y2 = 0 + 4x Remove the zero: 4xy + x2 + -5y + 4y2 = 4x Add '-4xy' to each side of the equation. 4xy + x2 + -5y + -4xy + 4y2 = 4x + -4xy Reorder the terms: 4xy + -4xy + x2 + -5y + 4y2 = 4x + -4xy Combine like terms: 4xy + -4xy = 0 0 + x2 + -5y + 4y2 = 4x + -4xy x2 + -5y + 4y2 = 4x + -4xy Add '-1x2' to each side of the equation. x2 + -5y + -1x2 + 4y2 = 4x + -4xy + -1x2 Reorder the terms: x2 + -1x2 + -5y + 4y2 = 4x + -4xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -5y + 4y2 = 4x + -4xy + -1x2 -5y + 4y2 = 4x + -4xy + -1x2 Add '5y' to each side of the equation. -5y + 5y + 4y2 = 4x + -4xy + -1x2 + 5y Combine like terms: -5y + 5y = 0 0 + 4y2 = 4x + -4xy + -1x2 + 5y 4y2 = 4x + -4xy + -1x2 + 5y Add '-4y2' to each side of the equation. 4y2 + -4y2 = 4x + -4xy + -1x2 + 5y + -4y2 Combine like terms: 4y2 + -4y2 = 0 0 = 4x + -4xy + -1x2 + 5y + -4y2 Simplifying 0 = 4x + -4xy + -1x2 + 5y + -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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