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Simplifying (2x2 + 2xy + y2) * dx + (x2 + 2xy) * dy = 0 Reorder the terms: (2xy + 2x2 + y2) * dx + (x2 + 2xy) * dy = 0 Reorder the terms for easier multiplication: dx(2xy + 2x2 + y2) + (x2 + 2xy) * dy = 0 (2xy * dx + 2x2 * dx + y2 * dx) + (x2 + 2xy) * dy = 0 Reorder the terms: (dxy2 + 2dx2y + 2dx3) + (x2 + 2xy) * dy = 0 (dxy2 + 2dx2y + 2dx3) + (x2 + 2xy) * dy = 0 Reorder the terms: dxy2 + 2dx2y + 2dx3 + (2xy + x2) * dy = 0 Reorder the terms for easier multiplication: dxy2 + 2dx2y + 2dx3 + dy(2xy + x2) = 0 dxy2 + 2dx2y + 2dx3 + (2xy * dy + x2 * dy) = 0 dxy2 + 2dx2y + 2dx3 + (2dxy2 + dx2y) = 0 Reorder the terms: dxy2 + 2dxy2 + 2dx2y + dx2y + 2dx3 = 0 Combine like terms: dxy2 + 2dxy2 = 3dxy2 3dxy2 + 2dx2y + dx2y + 2dx3 = 0 Combine like terms: 2dx2y + dx2y = 3dx2y 3dxy2 + 3dx2y + 2dx3 = 0 Solving 3dxy2 + 3dx2y + 2dx3 = 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(3y2 + 3xy + 2x2) = 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 '(3y2 + 3xy + 2x2)' equal to zero and attempt to solve: Simplifying 3y2 + 3xy + 2x2 = 0 Reorder the terms: 3xy + 2x2 + 3y2 = 0 Solving 3xy + 2x2 + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3xy' to each side of the equation. 3xy + 2x2 + -3xy + 3y2 = 0 + -3xy Reorder the terms: 3xy + -3xy + 2x2 + 3y2 = 0 + -3xy Combine like terms: 3xy + -3xy = 0 0 + 2x2 + 3y2 = 0 + -3xy 2x2 + 3y2 = 0 + -3xy Remove the zero: 2x2 + 3y2 = -3xy Add '-2x2' to each side of the equation. 2x2 + -2x2 + 3y2 = -3xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + 3y2 = -3xy + -2x2 3y2 = -3xy + -2x2 Add '-3y2' to each side of the equation. 3y2 + -3y2 = -3xy + -2x2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = -3xy + -2x2 + -3y2 Simplifying 0 = -3xy + -2x2 + -3y2 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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