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Simplifying (x + 2y + -4) * dx + (2x + y + -5) * dy = 0 Reorder the terms: (-4 + x + 2y) * dx + (2x + y + -5) * dy = 0 Reorder the terms for easier multiplication: dx(-4 + x + 2y) + (2x + y + -5) * dy = 0 (-4 * dx + x * dx + 2y * dx) + (2x + y + -5) * dy = 0 Reorder the terms: (-4dx + 2dxy + dx2) + (2x + y + -5) * dy = 0 (-4dx + 2dxy + dx2) + (2x + y + -5) * dy = 0 Reorder the terms: -4dx + 2dxy + dx2 + (-5 + 2x + y) * dy = 0 Reorder the terms for easier multiplication: -4dx + 2dxy + dx2 + dy(-5 + 2x + y) = 0 -4dx + 2dxy + dx2 + (-5 * dy + 2x * dy + y * dy) = 0 Reorder the terms: -4dx + 2dxy + dx2 + (2dxy + -5dy + dy2) = 0 -4dx + 2dxy + dx2 + (2dxy + -5dy + dy2) = 0 Reorder the terms: -4dx + 2dxy + 2dxy + dx2 + -5dy + dy2 = 0 Combine like terms: 2dxy + 2dxy = 4dxy -4dx + 4dxy + dx2 + -5dy + dy2 = 0 Solving -4dx + 4dxy + dx2 + -5dy + dy2 = 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 + y2) = 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 + y2)' equal to zero and attempt to solve: Simplifying -4x + 4xy + x2 + -5y + y2 = 0 Solving -4x + 4xy + x2 + -5y + y2 = 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 + y2 = 0 + 4x Reorder the terms: -4x + 4x + 4xy + x2 + -5y + y2 = 0 + 4x Combine like terms: -4x + 4x = 0 0 + 4xy + x2 + -5y + y2 = 0 + 4x 4xy + x2 + -5y + y2 = 0 + 4x Remove the zero: 4xy + x2 + -5y + y2 = 4x Add '-4xy' to each side of the equation. 4xy + x2 + -5y + -4xy + y2 = 4x + -4xy Reorder the terms: 4xy + -4xy + x2 + -5y + y2 = 4x + -4xy Combine like terms: 4xy + -4xy = 0 0 + x2 + -5y + y2 = 4x + -4xy x2 + -5y + y2 = 4x + -4xy Add '-1x2' to each side of the equation. x2 + -5y + -1x2 + y2 = 4x + -4xy + -1x2 Reorder the terms: x2 + -1x2 + -5y + y2 = 4x + -4xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -5y + y2 = 4x + -4xy + -1x2 -5y + y2 = 4x + -4xy + -1x2 Add '5y' to each side of the equation. -5y + 5y + y2 = 4x + -4xy + -1x2 + 5y Combine like terms: -5y + 5y = 0 0 + y2 = 4x + -4xy + -1x2 + 5y y2 = 4x + -4xy + -1x2 + 5y Add '-1y2' to each side of the equation. y2 + -1y2 = 4x + -4xy + -1x2 + 5y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = 4x + -4xy + -1x2 + 5y + -1y2 Simplifying 0 = 4x + -4xy + -1x2 + 5y + -1y2 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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