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Simplifying (x + y)(x + -1y) * dx + x(x + -2y) * dy = 0 Reorder the terms for easier multiplication: dx(x + y)(x + -1y) + x(x + -2y) * dy = 0 Multiply (x + y) * (x + -1y) dx(x(x + -1y) + y(x + -1y)) + x(x + -2y) * dy = 0 dx((x * x + -1y * x) + y(x + -1y)) + x(x + -2y) * dy = 0 Reorder the terms: dx((-1xy + x2) + y(x + -1y)) + x(x + -2y) * dy = 0 dx((-1xy + x2) + y(x + -1y)) + x(x + -2y) * dy = 0 dx(-1xy + x2 + (x * y + -1y * y)) + x(x + -2y) * dy = 0 dx(-1xy + x2 + (xy + -1y2)) + x(x + -2y) * dy = 0 Reorder the terms: dx(-1xy + xy + x2 + -1y2) + x(x + -2y) * dy = 0 Combine like terms: -1xy + xy = 0 dx(0 + x2 + -1y2) + x(x + -2y) * dy = 0 dx(x2 + -1y2) + x(x + -2y) * dy = 0 (x2 * dx + -1y2 * dx) + x(x + -2y) * dy = 0 Reorder the terms: (-1dxy2 + dx3) + x(x + -2y) * dy = 0 (-1dxy2 + dx3) + x(x + -2y) * dy = 0 Reorder the terms for easier multiplication: -1dxy2 + dx3 + x * dy(x + -2y) = 0 Multiply x * dy -1dxy2 + dx3 + dxy(x + -2y) = 0 -1dxy2 + dx3 + (x * dxy + -2y * dxy) = 0 Reorder the terms: -1dxy2 + dx3 + (-2dxy2 + dx2y) = 0 -1dxy2 + dx3 + (-2dxy2 + dx2y) = 0 Reorder the terms: -1dxy2 + -2dxy2 + dx2y + dx3 = 0 Combine like terms: -1dxy2 + -2dxy2 = -3dxy2 -3dxy2 + dx2y + dx3 = 0 Solving -3dxy2 + dx2y + dx3 = 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 + xy + x2) = 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 + xy + x2)' equal to zero and attempt to solve: Simplifying -3y2 + xy + x2 = 0 Reorder the terms: xy + x2 + -3y2 = 0 Solving xy + x2 + -3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1xy' to each side of the equation. xy + x2 + -1xy + -3y2 = 0 + -1xy Reorder the terms: xy + -1xy + x2 + -3y2 = 0 + -1xy Combine like terms: xy + -1xy = 0 0 + x2 + -3y2 = 0 + -1xy x2 + -3y2 = 0 + -1xy Remove the zero: x2 + -3y2 = -1xy Add '-1x2' to each side of the equation. x2 + -1x2 + -3y2 = -1xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -3y2 = -1xy + -1x2 -3y2 = -1xy + -1x2 Add '3y2' to each side of the equation. -3y2 + 3y2 = -1xy + -1x2 + 3y2 Combine like terms: -3y2 + 3y2 = 0 0 = -1xy + -1x2 + 3y2 Simplifying 0 = -1xy + -1x2 + 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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