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Simplifying (x + 2y + -8) * dx + (2x + 3y + -13) * dy = 0 Reorder the terms: (-8 + x + 2y) * dx + (2x + 3y + -13) * dy = 0 Reorder the terms for easier multiplication: dx(-8 + x + 2y) + (2x + 3y + -13) * dy = 0 (-8 * dx + x * dx + 2y * dx) + (2x + 3y + -13) * dy = 0 Reorder the terms: (-8dx + 2dxy + dx2) + (2x + 3y + -13) * dy = 0 (-8dx + 2dxy + dx2) + (2x + 3y + -13) * dy = 0 Reorder the terms: -8dx + 2dxy + dx2 + (-13 + 2x + 3y) * dy = 0 Reorder the terms for easier multiplication: -8dx + 2dxy + dx2 + dy(-13 + 2x + 3y) = 0 -8dx + 2dxy + dx2 + (-13 * dy + 2x * dy + 3y * dy) = 0 Reorder the terms: -8dx + 2dxy + dx2 + (2dxy + -13dy + 3dy2) = 0 -8dx + 2dxy + dx2 + (2dxy + -13dy + 3dy2) = 0 Reorder the terms: -8dx + 2dxy + 2dxy + dx2 + -13dy + 3dy2 = 0 Combine like terms: 2dxy + 2dxy = 4dxy -8dx + 4dxy + dx2 + -13dy + 3dy2 = 0 Solving -8dx + 4dxy + dx2 + -13dy + 3dy2 = 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 + 4xy + x2 + -13y + 3y2) = 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 + 4xy + x2 + -13y + 3y2)' equal to zero and attempt to solve: Simplifying -8x + 4xy + x2 + -13y + 3y2 = 0 Solving -8x + 4xy + x2 + -13y + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '8x' to each side of the equation. -8x + 4xy + x2 + -13y + 8x + 3y2 = 0 + 8x Reorder the terms: -8x + 8x + 4xy + x2 + -13y + 3y2 = 0 + 8x Combine like terms: -8x + 8x = 0 0 + 4xy + x2 + -13y + 3y2 = 0 + 8x 4xy + x2 + -13y + 3y2 = 0 + 8x Remove the zero: 4xy + x2 + -13y + 3y2 = 8x Add '-4xy' to each side of the equation. 4xy + x2 + -13y + -4xy + 3y2 = 8x + -4xy Reorder the terms: 4xy + -4xy + x2 + -13y + 3y2 = 8x + -4xy Combine like terms: 4xy + -4xy = 0 0 + x2 + -13y + 3y2 = 8x + -4xy x2 + -13y + 3y2 = 8x + -4xy Add '-1x2' to each side of the equation. x2 + -13y + -1x2 + 3y2 = 8x + -4xy + -1x2 Reorder the terms: x2 + -1x2 + -13y + 3y2 = 8x + -4xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -13y + 3y2 = 8x + -4xy + -1x2 -13y + 3y2 = 8x + -4xy + -1x2 Add '13y' to each side of the equation. -13y + 13y + 3y2 = 8x + -4xy + -1x2 + 13y Combine like terms: -13y + 13y = 0 0 + 3y2 = 8x + -4xy + -1x2 + 13y 3y2 = 8x + -4xy + -1x2 + 13y Add '-3y2' to each side of the equation. 3y2 + -3y2 = 8x + -4xy + -1x2 + 13y + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = 8x + -4xy + -1x2 + 13y + -3y2 Simplifying 0 = 8x + -4xy + -1x2 + 13y + -3y2 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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