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Simplifying (2x + -5y + 7) * dx + -1(5x + -12y + 8) * dy = 0 Reorder the terms: (7 + 2x + -5y) * dx + -1(5x + -12y + 8) * dy = 0 Reorder the terms for easier multiplication: dx(7 + 2x + -5y) + -1(5x + -12y + 8) * dy = 0 (7 * dx + 2x * dx + -5y * dx) + -1(5x + -12y + 8) * dy = 0 Reorder the terms: (7dx + -5dxy + 2dx2) + -1(5x + -12y + 8) * dy = 0 (7dx + -5dxy + 2dx2) + -1(5x + -12y + 8) * dy = 0 Reorder the terms: 7dx + -5dxy + 2dx2 + -1(8 + 5x + -12y) * dy = 0 Reorder the terms for easier multiplication: 7dx + -5dxy + 2dx2 + -1dy(8 + 5x + -12y) = 0 7dx + -5dxy + 2dx2 + (8 * -1dy + 5x * -1dy + -12y * -1dy) = 0 Reorder the terms: 7dx + -5dxy + 2dx2 + (-5dxy + -8dy + 12dy2) = 0 7dx + -5dxy + 2dx2 + (-5dxy + -8dy + 12dy2) = 0 Reorder the terms: 7dx + -5dxy + -5dxy + 2dx2 + -8dy + 12dy2 = 0 Combine like terms: -5dxy + -5dxy = -10dxy 7dx + -10dxy + 2dx2 + -8dy + 12dy2 = 0 Solving 7dx + -10dxy + 2dx2 + -8dy + 12dy2 = 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 + -10xy + 2x2 + -8y + 12y2) = 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 + -10xy + 2x2 + -8y + 12y2)' equal to zero and attempt to solve: Simplifying 7x + -10xy + 2x2 + -8y + 12y2 = 0 Solving 7x + -10xy + 2x2 + -8y + 12y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-7x' to each side of the equation. 7x + -10xy + 2x2 + -8y + -7x + 12y2 = 0 + -7x Reorder the terms: 7x + -7x + -10xy + 2x2 + -8y + 12y2 = 0 + -7x Combine like terms: 7x + -7x = 0 0 + -10xy + 2x2 + -8y + 12y2 = 0 + -7x -10xy + 2x2 + -8y + 12y2 = 0 + -7x Remove the zero: -10xy + 2x2 + -8y + 12y2 = -7x Add '10xy' to each side of the equation. -10xy + 2x2 + -8y + 10xy + 12y2 = -7x + 10xy Reorder the terms: -10xy + 10xy + 2x2 + -8y + 12y2 = -7x + 10xy Combine like terms: -10xy + 10xy = 0 0 + 2x2 + -8y + 12y2 = -7x + 10xy 2x2 + -8y + 12y2 = -7x + 10xy Add '-2x2' to each side of the equation. 2x2 + -8y + -2x2 + 12y2 = -7x + 10xy + -2x2 Reorder the terms: 2x2 + -2x2 + -8y + 12y2 = -7x + 10xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + -8y + 12y2 = -7x + 10xy + -2x2 -8y + 12y2 = -7x + 10xy + -2x2 Add '8y' to each side of the equation. -8y + 8y + 12y2 = -7x + 10xy + -2x2 + 8y Combine like terms: -8y + 8y = 0 0 + 12y2 = -7x + 10xy + -2x2 + 8y 12y2 = -7x + 10xy + -2x2 + 8y Add '-12y2' to each side of the equation. 12y2 + -12y2 = -7x + 10xy + -2x2 + 8y + -12y2 Combine like terms: 12y2 + -12y2 = 0 0 = -7x + 10xy + -2x2 + 8y + -12y2 Simplifying 0 = -7x + 10xy + -2x2 + 8y + -12y2 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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