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Simplifying (2x + -8y + 45) * dy + (16x + 2y + 54) * dx = 0 Reorder the terms: (45 + 2x + -8y) * dy + (16x + 2y + 54) * dx = 0 Reorder the terms for easier multiplication: dy(45 + 2x + -8y) + (16x + 2y + 54) * dx = 0 (45 * dy + 2x * dy + -8y * dy) + (16x + 2y + 54) * dx = 0 Reorder the terms: (2dxy + 45dy + -8dy2) + (16x + 2y + 54) * dx = 0 (2dxy + 45dy + -8dy2) + (16x + 2y + 54) * dx = 0 Reorder the terms: 2dxy + 45dy + -8dy2 + (54 + 16x + 2y) * dx = 0 Reorder the terms for easier multiplication: 2dxy + 45dy + -8dy2 + dx(54 + 16x + 2y) = 0 2dxy + 45dy + -8dy2 + (54 * dx + 16x * dx + 2y * dx) = 0 Reorder the terms: 2dxy + 45dy + -8dy2 + (54dx + 2dxy + 16dx2) = 0 2dxy + 45dy + -8dy2 + (54dx + 2dxy + 16dx2) = 0 Reorder the terms: 54dx + 2dxy + 2dxy + 16dx2 + 45dy + -8dy2 = 0 Combine like terms: 2dxy + 2dxy = 4dxy 54dx + 4dxy + 16dx2 + 45dy + -8dy2 = 0 Solving 54dx + 4dxy + 16dx2 + 45dy + -8dy2 = 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), 'd'. d(54x + 4xy + 16x2 + 45y + -8y2) = 0Subproblem 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 '(54x + 4xy + 16x2 + 45y + -8y2)' equal to zero and attempt to solve: Simplifying 54x + 4xy + 16x2 + 45y + -8y2 = 0 Solving 54x + 4xy + 16x2 + 45y + -8y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-54x' to each side of the equation. 54x + 4xy + 16x2 + 45y + -54x + -8y2 = 0 + -54x Reorder the terms: 54x + -54x + 4xy + 16x2 + 45y + -8y2 = 0 + -54x Combine like terms: 54x + -54x = 0 0 + 4xy + 16x2 + 45y + -8y2 = 0 + -54x 4xy + 16x2 + 45y + -8y2 = 0 + -54x Remove the zero: 4xy + 16x2 + 45y + -8y2 = -54x Add '-4xy' to each side of the equation. 4xy + 16x2 + 45y + -4xy + -8y2 = -54x + -4xy Reorder the terms: 4xy + -4xy + 16x2 + 45y + -8y2 = -54x + -4xy Combine like terms: 4xy + -4xy = 0 0 + 16x2 + 45y + -8y2 = -54x + -4xy 16x2 + 45y + -8y2 = -54x + -4xy Add '-16x2' to each side of the equation. 16x2 + 45y + -16x2 + -8y2 = -54x + -4xy + -16x2 Reorder the terms: 16x2 + -16x2 + 45y + -8y2 = -54x + -4xy + -16x2 Combine like terms: 16x2 + -16x2 = 0 0 + 45y + -8y2 = -54x + -4xy + -16x2 45y + -8y2 = -54x + -4xy + -16x2 Add '-45y' to each side of the equation. 45y + -45y + -8y2 = -54x + -4xy + -16x2 + -45y Combine like terms: 45y + -45y = 0 0 + -8y2 = -54x + -4xy + -16x2 + -45y -8y2 = -54x + -4xy + -16x2 + -45y Add '8y2' to each side of the equation. -8y2 + 8y2 = -54x + -4xy + -16x2 + -45y + 8y2 Combine like terms: -8y2 + 8y2 = 0 0 = -54x + -4xy + -16x2 + -45y + 8y2 Simplifying 0 = -54x + -4xy + -16x2 + -45y + 8y2 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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