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Simplifying (3x + 2y + -4) * dx + (33x + 2y + -5) * dy = 0 Reorder the terms: (-4 + 3x + 2y) * dx + (33x + 2y + -5) * dy = 0 Reorder the terms for easier multiplication: dx(-4 + 3x + 2y) + (33x + 2y + -5) * dy = 0 (-4 * dx + 3x * dx + 2y * dx) + (33x + 2y + -5) * dy = 0 Reorder the terms: (-4dx + 2dxy + 3dx2) + (33x + 2y + -5) * dy = 0 (-4dx + 2dxy + 3dx2) + (33x + 2y + -5) * dy = 0 Reorder the terms: -4dx + 2dxy + 3dx2 + (-5 + 33x + 2y) * dy = 0 Reorder the terms for easier multiplication: -4dx + 2dxy + 3dx2 + dy(-5 + 33x + 2y) = 0 -4dx + 2dxy + 3dx2 + (-5 * dy + 33x * dy + 2y * dy) = 0 Reorder the terms: -4dx + 2dxy + 3dx2 + (33dxy + -5dy + 2dy2) = 0 -4dx + 2dxy + 3dx2 + (33dxy + -5dy + 2dy2) = 0 Reorder the terms: -4dx + 2dxy + 33dxy + 3dx2 + -5dy + 2dy2 = 0 Combine like terms: 2dxy + 33dxy = 35dxy -4dx + 35dxy + 3dx2 + -5dy + 2dy2 = 0 Solving -4dx + 35dxy + 3dx2 + -5dy + 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 + 35xy + 3x2 + -5y + 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 + 35xy + 3x2 + -5y + 2y2)' equal to zero and attempt to solve: Simplifying -4x + 35xy + 3x2 + -5y + 2y2 = 0 Solving -4x + 35xy + 3x2 + -5y + 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 + 35xy + 3x2 + -5y + 4x + 2y2 = 0 + 4x Reorder the terms: -4x + 4x + 35xy + 3x2 + -5y + 2y2 = 0 + 4x Combine like terms: -4x + 4x = 0 0 + 35xy + 3x2 + -5y + 2y2 = 0 + 4x 35xy + 3x2 + -5y + 2y2 = 0 + 4x Remove the zero: 35xy + 3x2 + -5y + 2y2 = 4x Add '-35xy' to each side of the equation. 35xy + 3x2 + -5y + -35xy + 2y2 = 4x + -35xy Reorder the terms: 35xy + -35xy + 3x2 + -5y + 2y2 = 4x + -35xy Combine like terms: 35xy + -35xy = 0 0 + 3x2 + -5y + 2y2 = 4x + -35xy 3x2 + -5y + 2y2 = 4x + -35xy Add '-3x2' to each side of the equation. 3x2 + -5y + -3x2 + 2y2 = 4x + -35xy + -3x2 Reorder the terms: 3x2 + -3x2 + -5y + 2y2 = 4x + -35xy + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + -5y + 2y2 = 4x + -35xy + -3x2 -5y + 2y2 = 4x + -35xy + -3x2 Add '5y' to each side of the equation. -5y + 5y + 2y2 = 4x + -35xy + -3x2 + 5y Combine like terms: -5y + 5y = 0 0 + 2y2 = 4x + -35xy + -3x2 + 5y 2y2 = 4x + -35xy + -3x2 + 5y Add '-2y2' to each side of the equation. 2y2 + -2y2 = 4x + -35xy + -3x2 + 5y + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = 4x + -35xy + -3x2 + 5y + -2y2 Simplifying 0 = 4x + -35xy + -3x2 + 5y + -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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