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Simplifying (3x + -4y) * dy = (2x + 7y) * dx Reorder the terms for easier multiplication: dy(3x + -4y) = (2x + 7y) * dx (3x * dy + -4y * dy) = (2x + 7y) * dx (3dxy + -4dy2) = (2x + 7y) * dx Reorder the terms for easier multiplication: 3dxy + -4dy2 = dx(2x + 7y) 3dxy + -4dy2 = (2x * dx + 7y * dx) Reorder the terms: 3dxy + -4dy2 = (7dxy + 2dx2) 3dxy + -4dy2 = (7dxy + 2dx2) Solving 3dxy + -4dy2 = 7dxy + 2dx2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-7dxy' to each side of the equation. 3dxy + -7dxy + -4dy2 = 7dxy + -7dxy + 2dx2 Combine like terms: 3dxy + -7dxy = -4dxy -4dxy + -4dy2 = 7dxy + -7dxy + 2dx2 Combine like terms: 7dxy + -7dxy = 0 -4dxy + -4dy2 = 0 + 2dx2 -4dxy + -4dy2 = 2dx2 Add '-2dx2' to each side of the equation. -4dxy + -2dx2 + -4dy2 = 2dx2 + -2dx2 Combine like terms: 2dx2 + -2dx2 = 0 -4dxy + -2dx2 + -4dy2 = 0 Factor out the Greatest Common Factor (GCF), '-2d'. -2d(2xy + x2 + 2y2) = 0 Ignore the factor -2.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 '(2xy + x2 + 2y2)' equal to zero and attempt to solve: Simplifying 2xy + x2 + 2y2 = 0 Solving 2xy + x2 + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2xy' to each side of the equation. 2xy + x2 + -2xy + 2y2 = 0 + -2xy Reorder the terms: 2xy + -2xy + x2 + 2y2 = 0 + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 + 2y2 = 0 + -2xy x2 + 2y2 = 0 + -2xy Remove the zero: x2 + 2y2 = -2xy Add '-1x2' to each side of the equation. x2 + -1x2 + 2y2 = -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2y2 = -2xy + -1x2 2y2 = -2xy + -1x2 Add '-2y2' to each side of the equation. 2y2 + -2y2 = -2xy + -1x2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = -2xy + -1x2 + -2y2 Simplifying 0 = -2xy + -1x2 + -2y2 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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