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