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Simplifying 2xy(4 + -1y2) * dx + (y + -1)(x2 + 2) * dy = 0 Reorder the terms for easier multiplication: 2xy * dx(4 + -1y2) + (y + -1)(x2 + 2) * dy = 0 Multiply xy * dx 2dx2y(4 + -1y2) + (y + -1)(x2 + 2) * dy = 0 (4 * 2dx2y + -1y2 * 2dx2y) + (y + -1)(x2 + 2) * dy = 0 (8dx2y + -2dx2y3) + (y + -1)(x2 + 2) * dy = 0 Reorder the terms: 8dx2y + -2dx2y3 + (-1 + y)(x2 + 2) * dy = 0 Reorder the terms: 8dx2y + -2dx2y3 + (-1 + y)(2 + x2) * dy = 0 Reorder the terms for easier multiplication: 8dx2y + -2dx2y3 + dy(-1 + y)(2 + x2) = 0 Multiply (-1 + y) * (2 + x2) 8dx2y + -2dx2y3 + dy(-1(2 + x2) + y(2 + x2)) = 0 8dx2y + -2dx2y3 + dy((2 * -1 + x2 * -1) + y(2 + x2)) = 0 8dx2y + -2dx2y3 + dy((-2 + -1x2) + y(2 + x2)) = 0 8dx2y + -2dx2y3 + dy(-2 + -1x2 + (2 * y + x2 * y)) = 0 Reorder the terms: 8dx2y + -2dx2y3 + dy(-2 + -1x2 + (x2y + 2y)) = 0 8dx2y + -2dx2y3 + dy(-2 + -1x2 + (x2y + 2y)) = 0 8dx2y + -2dx2y3 + dy(-2 + -1x2 + x2y + 2y) = 0 8dx2y + -2dx2y3 + (-2 * dy + -1x2 * dy + x2y * dy + 2y * dy) = 0 Reorder the terms: 8dx2y + -2dx2y3 + (-1dx2y + dx2y2 + -2dy + 2dy2) = 0 8dx2y + -2dx2y3 + (-1dx2y + dx2y2 + -2dy + 2dy2) = 0 Reorder the terms: 8dx2y + -1dx2y + dx2y2 + -2dx2y3 + -2dy + 2dy2 = 0 Combine like terms: 8dx2y + -1dx2y = 7dx2y 7dx2y + dx2y2 + -2dx2y3 + -2dy + 2dy2 = 0 Solving 7dx2y + dx2y2 + -2dx2y3 + -2dy + 2dy2 = 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), 'dy'. dy(7x2 + x2y + -2x2y2 + -2 + 2y) = 0Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(7x2 + x2y + -2x2y2 + -2 + 2y)' equal to zero and attempt to solve: Simplifying 7x2 + x2y + -2x2y2 + -2 + 2y = 0 Reorder the terms: -2 + 7x2 + x2y + -2x2y2 + 2y = 0 Solving -2 + 7x2 + x2y + -2x2y2 + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 7x2 + x2y + -2x2y2 + 2 + 2y = 0 + 2 Reorder the terms: -2 + 2 + 7x2 + x2y + -2x2y2 + 2y = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7x2 + x2y + -2x2y2 + 2y = 0 + 2 7x2 + x2y + -2x2y2 + 2y = 0 + 2 Combine like terms: 0 + 2 = 2 7x2 + x2y + -2x2y2 + 2y = 2 Add '-7x2' to each side of the equation. 7x2 + x2y + -2x2y2 + -7x2 + 2y = 2 + -7x2 Reorder the terms: 7x2 + -7x2 + x2y + -2x2y2 + 2y = 2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 0 + x2y + -2x2y2 + 2y = 2 + -7x2 x2y + -2x2y2 + 2y = 2 + -7x2 Add '-1x2y' to each side of the equation. x2y + -2x2y2 + -1x2y + 2y = 2 + -7x2 + -1x2y Reorder the terms: x2y + -1x2y + -2x2y2 + 2y = 2 + -7x2 + -1x2y Combine like terms: x2y + -1x2y = 0 0 + -2x2y2 + 2y = 2 + -7x2 + -1x2y -2x2y2 + 2y = 2 + -7x2 + -1x2y Add '2x2y2' to each side of the equation. -2x2y2 + 2x2y2 + 2y = 2 + -7x2 + -1x2y + 2x2y2 Combine like terms: -2x2y2 + 2x2y2 = 0 0 + 2y = 2 + -7x2 + -1x2y + 2x2y2 2y = 2 + -7x2 + -1x2y + 2x2y2 Add '-2y' to each side of the equation. 2y + -2y = 2 + -7x2 + -1x2y + 2x2y2 + -2y Combine like terms: 2y + -2y = 0 0 = 2 + -7x2 + -1x2y + 2x2y2 + -2y Simplifying 0 = 2 + -7x2 + -1x2y + 2x2y2 + -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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