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Simplifying (2x + y) * dx + -1(4x + -1y) * dy = 0 Reorder the terms for easier multiplication: dx(2x + y) + -1(4x + -1y) * dy = 0 (2x * dx + y * dx) + -1(4x + -1y) * dy = 0 Reorder the terms: (dxy + 2dx2) + -1(4x + -1y) * dy = 0 (dxy + 2dx2) + -1(4x + -1y) * dy = 0 Reorder the terms for easier multiplication: dxy + 2dx2 + -1dy(4x + -1y) = 0 dxy + 2dx2 + (4x * -1dy + -1y * -1dy) = 0 dxy + 2dx2 + (-4dxy + 1dy2) = 0 Reorder the terms: dxy + -4dxy + 2dx2 + 1dy2 = 0 Combine like terms: dxy + -4dxy = -3dxy -3dxy + 2dx2 + 1dy2 = 0 Solving -3dxy + 2dx2 + 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(-3xy + 2x2 + y2) = 0 Factor a trinomial. d((x + -1y)(2x + -1y)) = 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 '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + -1y = 0 + -1x Combine like terms: x + -1x = 0 0 + -1y = 0 + -1x -1y = 0 + -1x Remove the zero: -1y = -1x Add 'y' to each side of the equation. -1y + y = -1x + y Combine like terms: -1y + y = 0 0 = -1x + y Simplifying 0 = -1x + y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + -1y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + -1y = 0 + -2x -1y = 0 + -2x Remove the zero: -1y = -2x Add 'y' to each side of the equation. -1y + y = -2x + y Combine like terms: -1y + y = 0 0 = -2x + y Simplifying 0 = -2x + y 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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