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