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Simplifying (x + y)(x + -1y) * dx + x(x + -2y) = 0 Reorder the terms for easier multiplication: dx(x + y)(x + -1y) + x(x + -2y) = 0 Multiply (x + y) * (x + -1y) dx(x(x + -1y) + y(x + -1y)) + x(x + -2y) = 0 dx((x * x + -1y * x) + y(x + -1y)) + x(x + -2y) = 0 Reorder the terms: dx((-1xy + x2) + y(x + -1y)) + x(x + -2y) = 0 dx((-1xy + x2) + y(x + -1y)) + x(x + -2y) = 0 dx(-1xy + x2 + (x * y + -1y * y)) + x(x + -2y) = 0 dx(-1xy + x2 + (xy + -1y2)) + x(x + -2y) = 0 Reorder the terms: dx(-1xy + xy + x2 + -1y2) + x(x + -2y) = 0 Combine like terms: -1xy + xy = 0 dx(0 + x2 + -1y2) + x(x + -2y) = 0 dx(x2 + -1y2) + x(x + -2y) = 0 (x2 * dx + -1y2 * dx) + x(x + -2y) = 0 Reorder the terms: (-1dxy2 + dx3) + x(x + -2y) = 0 (-1dxy2 + dx3) + x(x + -2y) = 0 -1dxy2 + dx3 + (x * x + -2y * x) = 0 Reorder the terms: -1dxy2 + dx3 + (-2xy + x2) = 0 -1dxy2 + dx3 + (-2xy + x2) = 0 Solving -1dxy2 + dx3 + -2xy + x2 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2xy' to each side of the equation. -1dxy2 + dx3 + -2xy + 2xy + x2 = 0 + 2xy Combine like terms: -2xy + 2xy = 0 -1dxy2 + dx3 + 0 + x2 = 0 + 2xy -1dxy2 + dx3 + x2 = 0 + 2xy Remove the zero: -1dxy2 + dx3 + x2 = 2xy Add '-1x2' to each side of the equation. -1dxy2 + dx3 + x2 + -1x2 = 2xy + -1x2 Combine like terms: x2 + -1x2 = 0 -1dxy2 + dx3 + 0 = 2xy + -1x2 -1dxy2 + dx3 = 2xy + -1x2 Reorder the terms: -1dxy2 + dx3 + -2xy + x2 = 2xy + -2xy + -1x2 + x2 Combine like terms: 2xy + -2xy = 0 -1dxy2 + dx3 + -2xy + x2 = 0 + -1x2 + x2 -1dxy2 + dx3 + -2xy + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -1dxy2 + dx3 + -2xy + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1dy2 + dx2 + -2y + x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 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 = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x 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 '(-1dy2 + dx2 + -2y + x)' equal to zero and attempt to solve: Simplifying -1dy2 + dx2 + -2y + x = 0 Reorder the terms: dx2 + -1dy2 + x + -2y = 0 Solving dx2 + -1dy2 + x + -2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. dx2 + -1dy2 + x + -1x + -2y = 0 + -1x Combine like terms: x + -1x = 0 dx2 + -1dy2 + 0 + -2y = 0 + -1x dx2 + -1dy2 + -2y = 0 + -1x Remove the zero: dx2 + -1dy2 + -2y = -1x Add '2y' to each side of the equation. dx2 + -1dy2 + -2y + 2y = -1x + 2y Combine like terms: -2y + 2y = 0 dx2 + -1dy2 + 0 = -1x + 2y dx2 + -1dy2 = -1x + 2y 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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