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Simplifying (3x + -7y + 7) * dx + -1(3x + -7y + -3) * dy = 0 Reorder the terms: (7 + 3x + -7y) * dx + -1(3x + -7y + -3) * dy = 0 Reorder the terms for easier multiplication: dx(7 + 3x + -7y) + -1(3x + -7y + -3) * dy = 0 (7 * dx + 3x * dx + -7y * dx) + -1(3x + -7y + -3) * dy = 0 Reorder the terms: (7dx + -7dxy + 3dx2) + -1(3x + -7y + -3) * dy = 0 (7dx + -7dxy + 3dx2) + -1(3x + -7y + -3) * dy = 0 Reorder the terms: 7dx + -7dxy + 3dx2 + -1(-3 + 3x + -7y) * dy = 0 Reorder the terms for easier multiplication: 7dx + -7dxy + 3dx2 + -1dy(-3 + 3x + -7y) = 0 7dx + -7dxy + 3dx2 + (-3 * -1dy + 3x * -1dy + -7y * -1dy) = 0 Reorder the terms: 7dx + -7dxy + 3dx2 + (-3dxy + 3dy + 7dy2) = 0 7dx + -7dxy + 3dx2 + (-3dxy + 3dy + 7dy2) = 0 Reorder the terms: 7dx + -7dxy + -3dxy + 3dx2 + 3dy + 7dy2 = 0 Combine like terms: -7dxy + -3dxy = -10dxy 7dx + -10dxy + 3dx2 + 3dy + 7dy2 = 0 Solving 7dx + -10dxy + 3dx2 + 3dy + 7dy2 = 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 + 3x2 + 3y + 7y2) = 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 + 3x2 + 3y + 7y2)' equal to zero and attempt to solve: Simplifying 7x + -10xy + 3x2 + 3y + 7y2 = 0 Solving 7x + -10xy + 3x2 + 3y + 7y2 = 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 + 3x2 + 3y + -7x + 7y2 = 0 + -7x Reorder the terms: 7x + -7x + -10xy + 3x2 + 3y + 7y2 = 0 + -7x Combine like terms: 7x + -7x = 0 0 + -10xy + 3x2 + 3y + 7y2 = 0 + -7x -10xy + 3x2 + 3y + 7y2 = 0 + -7x Remove the zero: -10xy + 3x2 + 3y + 7y2 = -7x Add '10xy' to each side of the equation. -10xy + 3x2 + 3y + 10xy + 7y2 = -7x + 10xy Reorder the terms: -10xy + 10xy + 3x2 + 3y + 7y2 = -7x + 10xy Combine like terms: -10xy + 10xy = 0 0 + 3x2 + 3y + 7y2 = -7x + 10xy 3x2 + 3y + 7y2 = -7x + 10xy Add '-3x2' to each side of the equation. 3x2 + 3y + -3x2 + 7y2 = -7x + 10xy + -3x2 Reorder the terms: 3x2 + -3x2 + 3y + 7y2 = -7x + 10xy + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + 3y + 7y2 = -7x + 10xy + -3x2 3y + 7y2 = -7x + 10xy + -3x2 Add '-3y' to each side of the equation. 3y + -3y + 7y2 = -7x + 10xy + -3x2 + -3y Combine like terms: 3y + -3y = 0 0 + 7y2 = -7x + 10xy + -3x2 + -3y 7y2 = -7x + 10xy + -3x2 + -3y Add '-7y2' to each side of the equation. 7y2 + -7y2 = -7x + 10xy + -3x2 + -3y + -7y2 Combine like terms: 7y2 + -7y2 = 0 0 = -7x + 10xy + -3x2 + -3y + -7y2 Simplifying 0 = -7x + 10xy + -3x2 + -3y + -7y2 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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