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Simplifying (4x + 3y + -7) * dx + (4x + 3y + 1) * dy = 0 Reorder the terms: (-7 + 4x + 3y) * dx + (4x + 3y + 1) * dy = 0 Reorder the terms for easier multiplication: dx(-7 + 4x + 3y) + (4x + 3y + 1) * dy = 0 (-7 * dx + 4x * dx + 3y * dx) + (4x + 3y + 1) * dy = 0 Reorder the terms: (-7dx + 3dxy + 4dx2) + (4x + 3y + 1) * dy = 0 (-7dx + 3dxy + 4dx2) + (4x + 3y + 1) * dy = 0 Reorder the terms: -7dx + 3dxy + 4dx2 + (1 + 4x + 3y) * dy = 0 Reorder the terms for easier multiplication: -7dx + 3dxy + 4dx2 + dy(1 + 4x + 3y) = 0 -7dx + 3dxy + 4dx2 + (1 * dy + 4x * dy + 3y * dy) = 0 Reorder the terms: -7dx + 3dxy + 4dx2 + (4dxy + 1dy + 3dy2) = 0 -7dx + 3dxy + 4dx2 + (4dxy + 1dy + 3dy2) = 0 Reorder the terms: -7dx + 3dxy + 4dxy + 4dx2 + 1dy + 3dy2 = 0 Combine like terms: 3dxy + 4dxy = 7dxy -7dx + 7dxy + 4dx2 + 1dy + 3dy2 = 0 Solving -7dx + 7dxy + 4dx2 + 1dy + 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(-7x + 7xy + 4x2 + y + 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 '(-7x + 7xy + 4x2 + y + 3y2)' equal to zero and attempt to solve: Simplifying -7x + 7xy + 4x2 + y + 3y2 = 0 Solving -7x + 7xy + 4x2 + y + 3y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '7x' to each side of the equation. -7x + 7xy + 4x2 + y + 7x + 3y2 = 0 + 7x Reorder the terms: -7x + 7x + 7xy + 4x2 + y + 3y2 = 0 + 7x Combine like terms: -7x + 7x = 0 0 + 7xy + 4x2 + y + 3y2 = 0 + 7x 7xy + 4x2 + y + 3y2 = 0 + 7x Remove the zero: 7xy + 4x2 + y + 3y2 = 7x Add '-7xy' to each side of the equation. 7xy + 4x2 + y + -7xy + 3y2 = 7x + -7xy Reorder the terms: 7xy + -7xy + 4x2 + y + 3y2 = 7x + -7xy Combine like terms: 7xy + -7xy = 0 0 + 4x2 + y + 3y2 = 7x + -7xy 4x2 + y + 3y2 = 7x + -7xy Add '-4x2' to each side of the equation. 4x2 + y + -4x2 + 3y2 = 7x + -7xy + -4x2 Reorder the terms: 4x2 + -4x2 + y + 3y2 = 7x + -7xy + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 + y + 3y2 = 7x + -7xy + -4x2 y + 3y2 = 7x + -7xy + -4x2 Add '-1y' to each side of the equation. y + -1y + 3y2 = 7x + -7xy + -4x2 + -1y Combine like terms: y + -1y = 0 0 + 3y2 = 7x + -7xy + -4x2 + -1y 3y2 = 7x + -7xy + -4x2 + -1y Add '-3y2' to each side of the equation. 3y2 + -3y2 = 7x + -7xy + -4x2 + -1y + -3y2 Combine like terms: 3y2 + -3y2 = 0 0 = 7x + -7xy + -4x2 + -1y + -3y2 Simplifying 0 = 7x + -7xy + -4x2 + -1y + -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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