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Simplifying 2(2y2 + 5xy + -2y + 4) * dx + x(x + 2y + -1) = 0 Reorder the terms: 2(4 + 5xy + -2y + 2y2) * dx + x(x + 2y + -1) = 0 Reorder the terms for easier multiplication: 2dx(4 + 5xy + -2y + 2y2) + x(x + 2y + -1) = 0 (4 * 2dx + 5xy * 2dx + -2y * 2dx + 2y2 * 2dx) + x(x + 2y + -1) = 0 Reorder the terms: (8dx + -4dxy + 4dxy2 + 10dx2y) + x(x + 2y + -1) = 0 (8dx + -4dxy + 4dxy2 + 10dx2y) + x(x + 2y + -1) = 0 Reorder the terms: 8dx + -4dxy + 4dxy2 + 10dx2y + x(-1 + x + 2y) = 0 8dx + -4dxy + 4dxy2 + 10dx2y + (-1 * x + x * x + 2y * x) = 0 Reorder the terms: 8dx + -4dxy + 4dxy2 + 10dx2y + (-1x + 2xy + x2) = 0 8dx + -4dxy + 4dxy2 + 10dx2y + (-1x + 2xy + x2) = 0 Solving 8dx + -4dxy + 4dxy2 + 10dx2y + -1x + 2xy + x2 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. 8dx + -4dxy + 4dxy2 + 10dx2y + -1x + 2xy + x + x2 = 0 + x Reorder the terms: 8dx + -4dxy + 4dxy2 + 10dx2y + -1x + x + 2xy + x2 = 0 + x Combine like terms: -1x + x = 0 8dx + -4dxy + 4dxy2 + 10dx2y + 0 + 2xy + x2 = 0 + x 8dx + -4dxy + 4dxy2 + 10dx2y + 2xy + x2 = 0 + x Remove the zero: 8dx + -4dxy + 4dxy2 + 10dx2y + 2xy + x2 = x Add '-2xy' to each side of the equation. 8dx + -4dxy + 4dxy2 + 10dx2y + 2xy + -2xy + x2 = x + -2xy Combine like terms: 2xy + -2xy = 0 8dx + -4dxy + 4dxy2 + 10dx2y + 0 + x2 = x + -2xy 8dx + -4dxy + 4dxy2 + 10dx2y + x2 = x + -2xy Add '-1x2' to each side of the equation. 8dx + -4dxy + 4dxy2 + 10dx2y + x2 + -1x2 = x + -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 8dx + -4dxy + 4dxy2 + 10dx2y + 0 = x + -2xy + -1x2 8dx + -4dxy + 4dxy2 + 10dx2y = x + -2xy + -1x2 Reorder the terms: 8dx + -4dxy + 4dxy2 + 10dx2y + -1x + 2xy + x2 = x + -1x + -2xy + 2xy + -1x2 + x2 Combine like terms: x + -1x = 0 8dx + -4dxy + 4dxy2 + 10dx2y + -1x + 2xy + x2 = 0 + -2xy + 2xy + -1x2 + x2 8dx + -4dxy + 4dxy2 + 10dx2y + -1x + 2xy + x2 = -2xy + 2xy + -1x2 + x2 Combine like terms: -2xy + 2xy = 0 8dx + -4dxy + 4dxy2 + 10dx2y + -1x + 2xy + x2 = 0 + -1x2 + x2 8dx + -4dxy + 4dxy2 + 10dx2y + -1x + 2xy + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 8dx + -4dxy + 4dxy2 + 10dx2y + -1x + 2xy + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(8d + -4dy + 4dy2 + 10dxy + -1 + 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 '(8d + -4dy + 4dy2 + 10dxy + -1 + 2y + x)' equal to zero and attempt to solve: Simplifying 8d + -4dy + 4dy2 + 10dxy + -1 + 2y + x = 0 Reorder the terms: -1 + 8d + 10dxy + -4dy + 4dy2 + x + 2y = 0 Solving -1 + 8d + 10dxy + -4dy + 4dy2 + x + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 8d + 10dxy + -4dy + 4dy2 + x + 1 + 2y = 0 + 1 Reorder the terms: -1 + 1 + 8d + 10dxy + -4dy + 4dy2 + x + 2y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 8d + 10dxy + -4dy + 4dy2 + x + 2y = 0 + 1 8d + 10dxy + -4dy + 4dy2 + x + 2y = 0 + 1 Combine like terms: 0 + 1 = 1 8d + 10dxy + -4dy + 4dy2 + x + 2y = 1 Add '-1x' to each side of the equation. 8d + 10dxy + -4dy + 4dy2 + x + -1x + 2y = 1 + -1x Combine like terms: x + -1x = 0 8d + 10dxy + -4dy + 4dy2 + 0 + 2y = 1 + -1x 8d + 10dxy + -4dy + 4dy2 + 2y = 1 + -1x Add '-2y' to each side of the equation. 8d + 10dxy + -4dy + 4dy2 + 2y + -2y = 1 + -1x + -2y Combine like terms: 2y + -2y = 0 8d + 10dxy + -4dy + 4dy2 + 0 = 1 + -1x + -2y 8d + 10dxy + -4dy + 4dy2 = 1 + -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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