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Simplifying (2x + -3y + -8) * dy + (-1x + -3y + -5) * dx = 0 Reorder the terms: (-8 + 2x + -3y) * dy + (-1x + -3y + -5) * dx = 0 Reorder the terms for easier multiplication: dy(-8 + 2x + -3y) + (-1x + -3y + -5) * dx = 0 (-8 * dy + 2x * dy + -3y * dy) + (-1x + -3y + -5) * dx = 0 Reorder the terms: (2dxy + -8dy + -3dy2) + (-1x + -3y + -5) * dx = 0 (2dxy + -8dy + -3dy2) + (-1x + -3y + -5) * dx = 0 Reorder the terms: 2dxy + -8dy + -3dy2 + (-5 + -1x + -3y) * dx = 0 Reorder the terms for easier multiplication: 2dxy + -8dy + -3dy2 + dx(-5 + -1x + -3y) = 0 2dxy + -8dy + -3dy2 + (-5 * dx + -1x * dx + -3y * dx) = 0 Reorder the terms: 2dxy + -8dy + -3dy2 + (-5dx + -3dxy + -1dx2) = 0 2dxy + -8dy + -3dy2 + (-5dx + -3dxy + -1dx2) = 0 Reorder the terms: -5dx + 2dxy + -3dxy + -1dx2 + -8dy + -3dy2 = 0 Combine like terms: 2dxy + -3dxy = -1dxy -5dx + -1dxy + -1dx2 + -8dy + -3dy2 = 0 Solving -5dx + -1dxy + -1dx2 + -8dy + -3dy2 = 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), '-1d'. -1d(5x + xy + x2 + 8y + 3y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(5x + xy + x2 + 8y + 3y2)' equal to zero and attempt to solve: Simplifying 5x + xy + x2 + 8y + 3y2 = 0 Solving 5x + xy + x2 + 8y + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-5x' to each side of the equation. 5x + xy + x2 + 8y + -5x + 3y2 = 0 + -5x Reorder the terms: 5x + -5x + xy + x2 + 8y + 3y2 = 0 + -5x Combine like terms: 5x + -5x = 0 0 + xy + x2 + 8y + 3y2 = 0 + -5x xy + x2 + 8y + 3y2 = 0 + -5x Remove the zero: xy + x2 + 8y + 3y2 = -5x Add '-1xy' to each side of the equation. xy + x2 + 8y + -1xy + 3y2 = -5x + -1xy Reorder the terms: xy + -1xy + x2 + 8y + 3y2 = -5x + -1xy Combine like terms: xy + -1xy = 0 0 + x2 + 8y + 3y2 = -5x + -1xy x2 + 8y + 3y2 = -5x + -1xy Add '-1x2' to each side of the equation. x2 + 8y + -1x2 + 3y2 = -5x + -1xy + -1x2 Reorder the terms: x2 + -1x2 + 8y + 3y2 = -5x + -1xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 8y + 3y2 = -5x + -1xy + -1x2 8y + 3y2 = -5x + -1xy + -1x2 Add '-8y' to each side of the equation. 8y + -8y + 3y2 = -5x + -1xy + -1x2 + -8y Combine like terms: 8y + -8y = 0 0 + 3y2 = -5x + -1xy + -1x2 + -8y 3y2 = -5x + -1xy + -1x2 + -8y Add '-3y2' to each side of the equation. 3y2 + -3y2 = -5x + -1xy + -1x2 + -8y + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = -5x + -1xy + -1x2 + -8y + -3y2 Simplifying 0 = -5x + -1xy + -1x2 + -8y + -3y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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