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