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Simplifying (2x + -3y) * dx + (5y + -1x) * dy = 0 Reorder the terms for easier multiplication: dx(2x + -3y) + (5y + -1x) * dy = 0 (2x * dx + -3y * dx) + (5y + -1x) * dy = 0 Reorder the terms: (-3dxy + 2dx2) + (5y + -1x) * dy = 0 (-3dxy + 2dx2) + (5y + -1x) * dy = 0 Reorder the terms: -3dxy + 2dx2 + (-1x + 5y) * dy = 0 Reorder the terms for easier multiplication: -3dxy + 2dx2 + dy(-1x + 5y) = 0 -3dxy + 2dx2 + (-1x * dy + 5y * dy) = 0 -3dxy + 2dx2 + (-1dxy + 5dy2) = 0 Reorder the terms: -3dxy + -1dxy + 2dx2 + 5dy2 = 0 Combine like terms: -3dxy + -1dxy = -4dxy -4dxy + 2dx2 + 5dy2 = 0 Solving -4dxy + 2dx2 + 5dy2 = 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(-4xy + 2x2 + 5y2) = 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 '(-4xy + 2x2 + 5y2)' equal to zero and attempt to solve: Simplifying -4xy + 2x2 + 5y2 = 0 Solving -4xy + 2x2 + 5y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '4xy' to each side of the equation. -4xy + 2x2 + 4xy + 5y2 = 0 + 4xy Reorder the terms: -4xy + 4xy + 2x2 + 5y2 = 0 + 4xy Combine like terms: -4xy + 4xy = 0 0 + 2x2 + 5y2 = 0 + 4xy 2x2 + 5y2 = 0 + 4xy Remove the zero: 2x2 + 5y2 = 4xy Add '-2x2' to each side of the equation. 2x2 + -2x2 + 5y2 = 4xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + 5y2 = 4xy + -2x2 5y2 = 4xy + -2x2 Add '-5y2' to each side of the equation. 5y2 + -5y2 = 4xy + -2x2 + -5y2 Combine like terms: 5y2 + -5y2 = 0 0 = 4xy + -2x2 + -5y2 Simplifying 0 = 4xy + -2x2 + -5y2 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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