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Simplifying (5x + 4y + 1) * dy + -1(2x + 3y + 8) * dx = 0 Reorder the terms: (1 + 5x + 4y) * dy + -1(2x + 3y + 8) * dx = 0 Reorder the terms for easier multiplication: dy(1 + 5x + 4y) + -1(2x + 3y + 8) * dx = 0 (1 * dy + 5x * dy + 4y * dy) + -1(2x + 3y + 8) * dx = 0 Reorder the terms: (5dxy + 1dy + 4dy2) + -1(2x + 3y + 8) * dx = 0 (5dxy + 1dy + 4dy2) + -1(2x + 3y + 8) * dx = 0 Reorder the terms: 5dxy + 1dy + 4dy2 + -1(8 + 2x + 3y) * dx = 0 Reorder the terms for easier multiplication: 5dxy + 1dy + 4dy2 + -1dx(8 + 2x + 3y) = 0 5dxy + 1dy + 4dy2 + (8 * -1dx + 2x * -1dx + 3y * -1dx) = 0 Reorder the terms: 5dxy + 1dy + 4dy2 + (-8dx + -3dxy + -2dx2) = 0 5dxy + 1dy + 4dy2 + (-8dx + -3dxy + -2dx2) = 0 Reorder the terms: -8dx + 5dxy + -3dxy + -2dx2 + 1dy + 4dy2 = 0 Combine like terms: 5dxy + -3dxy = 2dxy -8dx + 2dxy + -2dx2 + 1dy + 4dy2 = 0 Solving -8dx + 2dxy + -2dx2 + 1dy + 4dy2 = 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(-8x + 2xy + -2x2 + y + 4y2) = 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 '(-8x + 2xy + -2x2 + y + 4y2)' equal to zero and attempt to solve: Simplifying -8x + 2xy + -2x2 + y + 4y2 = 0 Solving -8x + 2xy + -2x2 + y + 4y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '8x' to each side of the equation. -8x + 2xy + -2x2 + y + 8x + 4y2 = 0 + 8x Reorder the terms: -8x + 8x + 2xy + -2x2 + y + 4y2 = 0 + 8x Combine like terms: -8x + 8x = 0 0 + 2xy + -2x2 + y + 4y2 = 0 + 8x 2xy + -2x2 + y + 4y2 = 0 + 8x Remove the zero: 2xy + -2x2 + y + 4y2 = 8x Add '-2xy' to each side of the equation. 2xy + -2x2 + y + -2xy + 4y2 = 8x + -2xy Reorder the terms: 2xy + -2xy + -2x2 + y + 4y2 = 8x + -2xy Combine like terms: 2xy + -2xy = 0 0 + -2x2 + y + 4y2 = 8x + -2xy -2x2 + y + 4y2 = 8x + -2xy Add '2x2' to each side of the equation. -2x2 + y + 2x2 + 4y2 = 8x + -2xy + 2x2 Reorder the terms: -2x2 + 2x2 + y + 4y2 = 8x + -2xy + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 + y + 4y2 = 8x + -2xy + 2x2 y + 4y2 = 8x + -2xy + 2x2 Add '-1y' to each side of the equation. y + -1y + 4y2 = 8x + -2xy + 2x2 + -1y Combine like terms: y + -1y = 0 0 + 4y2 = 8x + -2xy + 2x2 + -1y 4y2 = 8x + -2xy + 2x2 + -1y Add '-4y2' to each side of the equation. 4y2 + -4y2 = 8x + -2xy + 2x2 + -1y + -4y2 Combine like terms: 4y2 + -4y2 = 0 0 = 8x + -2xy + 2x2 + -1y + -4y2 Simplifying 0 = 8x + -2xy + 2x2 + -1y + -4y2 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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