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