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Simplifying (x + -1y)(4x + y) * dx + x(5x + -1xy) * dy = 0 Reorder the terms for easier multiplication: dx(x + -1y)(4x + y) + x(5x + -1xy) * dy = 0 Multiply (x + -1y) * (4x + y) dx(x(4x + y) + -1y * (4x + y)) + x(5x + -1xy) * dy = 0 dx((4x * x + y * x) + -1y * (4x + y)) + x(5x + -1xy) * dy = 0 Reorder the terms: dx((xy + 4x2) + -1y * (4x + y)) + x(5x + -1xy) * dy = 0 dx((xy + 4x2) + -1y * (4x + y)) + x(5x + -1xy) * dy = 0 dx(xy + 4x2 + (4x * -1y + y * -1y)) + x(5x + -1xy) * dy = 0 dx(xy + 4x2 + (-4xy + -1y2)) + x(5x + -1xy) * dy = 0 Reorder the terms: dx(xy + -4xy + 4x2 + -1y2) + x(5x + -1xy) * dy = 0 Combine like terms: xy + -4xy = -3xy dx(-3xy + 4x2 + -1y2) + x(5x + -1xy) * dy = 0 (-3xy * dx + 4x2 * dx + -1y2 * dx) + x(5x + -1xy) * dy = 0 Reorder the terms: (-1dxy2 + -3dx2y + 4dx3) + x(5x + -1xy) * dy = 0 (-1dxy2 + -3dx2y + 4dx3) + x(5x + -1xy) * dy = 0 Reorder the terms for easier multiplication: -1dxy2 + -3dx2y + 4dx3 + x * dy(5x + -1xy) = 0 Multiply x * dy -1dxy2 + -3dx2y + 4dx3 + dxy(5x + -1xy) = 0 -1dxy2 + -3dx2y + 4dx3 + (5x * dxy + -1xy * dxy) = 0 -1dxy2 + -3dx2y + 4dx3 + (5dx2y + -1dx2y2) = 0 Reorder the terms: -1dxy2 + -3dx2y + 5dx2y + -1dx2y2 + 4dx3 = 0 Combine like terms: -3dx2y + 5dx2y = 2dx2y -1dxy2 + 2dx2y + -1dx2y2 + 4dx3 = 0 Solving -1dxy2 + 2dx2y + -1dx2y2 + 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(-1y2 + 2xy + -1xy2 + 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 '(-1y2 + 2xy + -1xy2 + 4x2)' equal to zero and attempt to solve: Simplifying -1y2 + 2xy + -1xy2 + 4x2 = 0 Reorder the terms: 2xy + -1xy2 + 4x2 + -1y2 = 0 Solving 2xy + -1xy2 + 4x2 + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2xy' to each side of the equation. 2xy + -1xy2 + 4x2 + -2xy + -1y2 = 0 + -2xy Reorder the terms: 2xy + -2xy + -1xy2 + 4x2 + -1y2 = 0 + -2xy Combine like terms: 2xy + -2xy = 0 0 + -1xy2 + 4x2 + -1y2 = 0 + -2xy -1xy2 + 4x2 + -1y2 = 0 + -2xy Remove the zero: -1xy2 + 4x2 + -1y2 = -2xy Add 'xy2' to each side of the equation. -1xy2 + 4x2 + xy2 + -1y2 = -2xy + xy2 Reorder the terms: -1xy2 + xy2 + 4x2 + -1y2 = -2xy + xy2 Combine like terms: -1xy2 + xy2 = 0 0 + 4x2 + -1y2 = -2xy + xy2 4x2 + -1y2 = -2xy + xy2 Add '-4x2' to each side of the equation. 4x2 + -4x2 + -1y2 = -2xy + xy2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 + -1y2 = -2xy + xy2 + -4x2 -1y2 = -2xy + xy2 + -4x2 Add 'y2' to each side of the equation. -1y2 + y2 = -2xy + xy2 + -4x2 + y2 Combine like terms: -1y2 + y2 = 0 0 = -2xy + xy2 + -4x2 + y2 Simplifying 0 = -2xy + xy2 + -4x2 + y2 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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