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Simplifying (4x2 + -4xy + 3y2 + -3y + 2) * dx + x(2x + -2y + 1) * dy = 0 Reorder the terms: (2 + -4xy + 4x2 + -3y + 3y2) * dx + x(2x + -2y + 1) * dy = 0 Reorder the terms for easier multiplication: dx(2 + -4xy + 4x2 + -3y + 3y2) + x(2x + -2y + 1) * dy = 0 (2 * dx + -4xy * dx + 4x2 * dx + -3y * dx + 3y2 * dx) + x(2x + -2y + 1) * dy = 0 Reorder the terms: (2dx + -3dxy + 3dxy2 + -4dx2y + 4dx3) + x(2x + -2y + 1) * dy = 0 (2dx + -3dxy + 3dxy2 + -4dx2y + 4dx3) + x(2x + -2y + 1) * dy = 0 Reorder the terms: 2dx + -3dxy + 3dxy2 + -4dx2y + 4dx3 + x(1 + 2x + -2y) * dy = 0 Reorder the terms for easier multiplication: 2dx + -3dxy + 3dxy2 + -4dx2y + 4dx3 + x * dy(1 + 2x + -2y) = 0 Multiply x * dy 2dx + -3dxy + 3dxy2 + -4dx2y + 4dx3 + dxy(1 + 2x + -2y) = 0 2dx + -3dxy + 3dxy2 + -4dx2y + 4dx3 + (1 * dxy + 2x * dxy + -2y * dxy) = 0 Reorder the terms: 2dx + -3dxy + 3dxy2 + -4dx2y + 4dx3 + (1dxy + -2dxy2 + 2dx2y) = 0 2dx + -3dxy + 3dxy2 + -4dx2y + 4dx3 + (1dxy + -2dxy2 + 2dx2y) = 0 Reorder the terms: 2dx + -3dxy + 1dxy + 3dxy2 + -2dxy2 + -4dx2y + 2dx2y + 4dx3 = 0 Combine like terms: -3dxy + 1dxy = -2dxy 2dx + -2dxy + 3dxy2 + -2dxy2 + -4dx2y + 2dx2y + 4dx3 = 0 Combine like terms: 3dxy2 + -2dxy2 = 1dxy2 2dx + -2dxy + 1dxy2 + -4dx2y + 2dx2y + 4dx3 = 0 Combine like terms: -4dx2y + 2dx2y = -2dx2y 2dx + -2dxy + 1dxy2 + -2dx2y + 4dx3 = 0 Solving 2dx + -2dxy + 1dxy2 + -2dx2y + 4dx3 = 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), 'dx'. dx(2 + -2y + y2 + -2xy + 4x2) = 0Subproblem 1
Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2 + -2y + y2 + -2xy + 4x2)' equal to zero and attempt to solve: Simplifying 2 + -2y + y2 + -2xy + 4x2 = 0 Reorder the terms: 2 + -2xy + 4x2 + -2y + y2 = 0 Solving 2 + -2xy + 4x2 + -2y + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2xy + 4x2 + -2y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -2xy + 4x2 + -2y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2xy + 4x2 + -2y + y2 = 0 + -2 -2xy + 4x2 + -2y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2xy + 4x2 + -2y + y2 = -2 Add '2xy' to each side of the equation. -2xy + 4x2 + -2y + 2xy + y2 = -2 + 2xy Reorder the terms: -2xy + 2xy + 4x2 + -2y + y2 = -2 + 2xy Combine like terms: -2xy + 2xy = 0 0 + 4x2 + -2y + y2 = -2 + 2xy 4x2 + -2y + y2 = -2 + 2xy Add '-4x2' to each side of the equation. 4x2 + -2y + -4x2 + y2 = -2 + 2xy + -4x2 Reorder the terms: 4x2 + -4x2 + -2y + y2 = -2 + 2xy + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 + -2y + y2 = -2 + 2xy + -4x2 -2y + y2 = -2 + 2xy + -4x2 Add '2y' to each side of the equation. -2y + 2y + y2 = -2 + 2xy + -4x2 + 2y Combine like terms: -2y + 2y = 0 0 + y2 = -2 + 2xy + -4x2 + 2y y2 = -2 + 2xy + -4x2 + 2y Add '-1y2' to each side of the equation. y2 + -1y2 = -2 + 2xy + -4x2 + 2y + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -2 + 2xy + -4x2 + 2y + -1y2 Simplifying 0 = -2 + 2xy + -4x2 + 2y + -1y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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