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