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