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Simplifying (3x + 4y + -7) * dx + (6[3x + 4y] + 2) * dy = 0 Reorder the terms: (-7 + 3x + 4y) * dx + (6[3x + 4y] + 2) * dy = 0 Reorder the terms for easier multiplication: dx(-7 + 3x + 4y) + (6[3x + 4y] + 2) * dy = 0 (-7 * dx + 3x * dx + 4y * dx) + (6[3x + 4y] + 2) * dy = 0 Reorder the terms: (-7dx + 4dxy + 3dx2) + (6[3x + 4y] + 2) * dy = 0 (-7dx + 4dxy + 3dx2) + (6[3x + 4y] + 2) * dy = 0 -7dx + 4dxy + 3dx2 + ([3x * 6 + 4y * 6] + 2) * dy = 0 -7dx + 4dxy + 3dx2 + ([18x + 24y] + 2) * dy = 0 Reorder the terms: -7dx + 4dxy + 3dx2 + (2 + 18x + 24y) * dy = 0 Reorder the terms for easier multiplication: -7dx + 4dxy + 3dx2 + dy(2 + 18x + 24y) = 0 -7dx + 4dxy + 3dx2 + (2 * dy + 18x * dy + 24y * dy) = 0 Reorder the terms: -7dx + 4dxy + 3dx2 + (18dxy + 2dy + 24dy2) = 0 -7dx + 4dxy + 3dx2 + (18dxy + 2dy + 24dy2) = 0 Reorder the terms: -7dx + 4dxy + 18dxy + 3dx2 + 2dy + 24dy2 = 0 Combine like terms: 4dxy + 18dxy = 22dxy -7dx + 22dxy + 3dx2 + 2dy + 24dy2 = 0 Solving -7dx + 22dxy + 3dx2 + 2dy + 24dy2 = 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 + 22xy + 3x2 + 2y + 24y2) = 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 + 22xy + 3x2 + 2y + 24y2)' equal to zero and attempt to solve: Simplifying -7x + 22xy + 3x2 + 2y + 24y2 = 0 Solving -7x + 22xy + 3x2 + 2y + 24y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '7x' to each side of the equation. -7x + 22xy + 3x2 + 2y + 7x + 24y2 = 0 + 7x Reorder the terms: -7x + 7x + 22xy + 3x2 + 2y + 24y2 = 0 + 7x Combine like terms: -7x + 7x = 0 0 + 22xy + 3x2 + 2y + 24y2 = 0 + 7x 22xy + 3x2 + 2y + 24y2 = 0 + 7x Remove the zero: 22xy + 3x2 + 2y + 24y2 = 7x Add '-22xy' to each side of the equation. 22xy + 3x2 + 2y + -22xy + 24y2 = 7x + -22xy Reorder the terms: 22xy + -22xy + 3x2 + 2y + 24y2 = 7x + -22xy Combine like terms: 22xy + -22xy = 0 0 + 3x2 + 2y + 24y2 = 7x + -22xy 3x2 + 2y + 24y2 = 7x + -22xy Add '-3x2' to each side of the equation. 3x2 + 2y + -3x2 + 24y2 = 7x + -22xy + -3x2 Reorder the terms: 3x2 + -3x2 + 2y + 24y2 = 7x + -22xy + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + 2y + 24y2 = 7x + -22xy + -3x2 2y + 24y2 = 7x + -22xy + -3x2 Add '-2y' to each side of the equation. 2y + -2y + 24y2 = 7x + -22xy + -3x2 + -2y Combine like terms: 2y + -2y = 0 0 + 24y2 = 7x + -22xy + -3x2 + -2y 24y2 = 7x + -22xy + -3x2 + -2y Add '-24y2' to each side of the equation. 24y2 + -24y2 = 7x + -22xy + -3x2 + -2y + -24y2 Combine like terms: 24y2 + -24y2 = 0 0 = 7x + -22xy + -3x2 + -2y + -24y2 Simplifying 0 = 7x + -22xy + -3x2 + -2y + -24y2 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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