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