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