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Simplifying (3x + 4y + 1) * dy + (2x + 3y + 1) * dx = 0 Reorder the terms: (1 + 3x + 4y) * dy + (2x + 3y + 1) * dx = 0 Reorder the terms for easier multiplication: dy(1 + 3x + 4y) + (2x + 3y + 1) * dx = 0 (1 * dy + 3x * dy + 4y * dy) + (2x + 3y + 1) * dx = 0 Reorder the terms: (3dxy + 1dy + 4dy2) + (2x + 3y + 1) * dx = 0 (3dxy + 1dy + 4dy2) + (2x + 3y + 1) * dx = 0 Reorder the terms: 3dxy + 1dy + 4dy2 + (1 + 2x + 3y) * dx = 0 Reorder the terms for easier multiplication: 3dxy + 1dy + 4dy2 + dx(1 + 2x + 3y) = 0 3dxy + 1dy + 4dy2 + (1 * dx + 2x * dx + 3y * dx) = 0 Reorder the terms: 3dxy + 1dy + 4dy2 + (1dx + 3dxy + 2dx2) = 0 3dxy + 1dy + 4dy2 + (1dx + 3dxy + 2dx2) = 0 Reorder the terms: 1dx + 3dxy + 3dxy + 2dx2 + 1dy + 4dy2 = 0 Combine like terms: 3dxy + 3dxy = 6dxy 1dx + 6dxy + 2dx2 + 1dy + 4dy2 = 0 Solving 1dx + 6dxy + 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(x + 6xy + 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 '(x + 6xy + 2x2 + y + 4y2)' equal to zero and attempt to solve: Simplifying x + 6xy + 2x2 + y + 4y2 = 0 Solving x + 6xy + 2x2 + y + 4y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + 6xy + 2x2 + y + -1x + 4y2 = 0 + -1x Reorder the terms: x + -1x + 6xy + 2x2 + y + 4y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + 6xy + 2x2 + y + 4y2 = 0 + -1x 6xy + 2x2 + y + 4y2 = 0 + -1x Remove the zero: 6xy + 2x2 + y + 4y2 = -1x Add '-6xy' to each side of the equation. 6xy + 2x2 + y + -6xy + 4y2 = -1x + -6xy Reorder the terms: 6xy + -6xy + 2x2 + y + 4y2 = -1x + -6xy Combine like terms: 6xy + -6xy = 0 0 + 2x2 + y + 4y2 = -1x + -6xy 2x2 + y + 4y2 = -1x + -6xy Add '-2x2' to each side of the equation. 2x2 + y + -2x2 + 4y2 = -1x + -6xy + -2x2 Reorder the terms: 2x2 + -2x2 + y + 4y2 = -1x + -6xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + y + 4y2 = -1x + -6xy + -2x2 y + 4y2 = -1x + -6xy + -2x2 Add '-1y' to each side of the equation. y + -1y + 4y2 = -1x + -6xy + -2x2 + -1y Combine like terms: y + -1y = 0 0 + 4y2 = -1x + -6xy + -2x2 + -1y 4y2 = -1x + -6xy + -2x2 + -1y Add '-4y2' to each side of the equation. 4y2 + -4y2 = -1x + -6xy + -2x2 + -1y + -4y2 Combine like terms: 4y2 + -4y2 = 0 0 = -1x + -6xy + -2x2 + -1y + -4y2 Simplifying 0 = -1x + -6xy + -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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