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Simplifying (2x5 + 3y2 + -7) * x * dx + -1(3x2 + 2y2 + -8) * y * dy = 0 Reorder the terms: (-7 + 2x5 + 3y2) * x * dx + -1(3x2 + 2y2 + -8) * y * dy = 0 Reorder the terms for easier multiplication: x * dx(-7 + 2x5 + 3y2) + -1(3x2 + 2y2 + -8) * y * dy = 0 Multiply x * dx dx2(-7 + 2x5 + 3y2) + -1(3x2 + 2y2 + -8) * y * dy = 0 (-7 * dx2 + 2x5 * dx2 + 3y2 * dx2) + -1(3x2 + 2y2 + -8) * y * dy = 0 Reorder the terms: (-7dx2 + 3dx2y2 + 2dx7) + -1(3x2 + 2y2 + -8) * y * dy = 0 (-7dx2 + 3dx2y2 + 2dx7) + -1(3x2 + 2y2 + -8) * y * dy = 0 Reorder the terms: -7dx2 + 3dx2y2 + 2dx7 + -1(-8 + 3x2 + 2y2) * y * dy = 0 Reorder the terms for easier multiplication: -7dx2 + 3dx2y2 + 2dx7 + -1y * dy(-8 + 3x2 + 2y2) = 0 Multiply y * dy -7dx2 + 3dx2y2 + 2dx7 + -1dy2(-8 + 3x2 + 2y2) = 0 -7dx2 + 3dx2y2 + 2dx7 + (-8 * -1dy2 + 3x2 * -1dy2 + 2y2 * -1dy2) = 0 Reorder the terms: -7dx2 + 3dx2y2 + 2dx7 + (-3dx2y2 + 8dy2 + -2dy4) = 0 -7dx2 + 3dx2y2 + 2dx7 + (-3dx2y2 + 8dy2 + -2dy4) = 0 Reorder the terms: -7dx2 + 3dx2y2 + -3dx2y2 + 2dx7 + 8dy2 + -2dy4 = 0 Combine like terms: 3dx2y2 + -3dx2y2 = 0 -7dx2 + 0 + 2dx7 + 8dy2 + -2dy4 = 0 -7dx2 + 2dx7 + 8dy2 + -2dy4 = 0 Solving -7dx2 + 2dx7 + 8dy2 + -2dy4 = 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(-7x2 + 2x7 + 8y2 + -2y4) = 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 '(-7x2 + 2x7 + 8y2 + -2y4)' equal to zero and attempt to solve: Simplifying -7x2 + 2x7 + 8y2 + -2y4 = 0 Solving -7x2 + 2x7 + 8y2 + -2y4 = 0 Move all terms containing d to the left, all other terms to the right. Add '7x2' to each side of the equation. -7x2 + 2x7 + 8y2 + 7x2 + -2y4 = 0 + 7x2 Reorder the terms: -7x2 + 7x2 + 2x7 + 8y2 + -2y4 = 0 + 7x2 Combine like terms: -7x2 + 7x2 = 0 0 + 2x7 + 8y2 + -2y4 = 0 + 7x2 2x7 + 8y2 + -2y4 = 0 + 7x2 Remove the zero: 2x7 + 8y2 + -2y4 = 7x2 Add '-2x7' to each side of the equation. 2x7 + 8y2 + -2x7 + -2y4 = 7x2 + -2x7 Reorder the terms: 2x7 + -2x7 + 8y2 + -2y4 = 7x2 + -2x7 Combine like terms: 2x7 + -2x7 = 0 0 + 8y2 + -2y4 = 7x2 + -2x7 8y2 + -2y4 = 7x2 + -2x7 Add '-8y2' to each side of the equation. 8y2 + -8y2 + -2y4 = 7x2 + -2x7 + -8y2 Combine like terms: 8y2 + -8y2 = 0 0 + -2y4 = 7x2 + -2x7 + -8y2 -2y4 = 7x2 + -2x7 + -8y2 Add '2y4' to each side of the equation. -2y4 + 2y4 = 7x2 + -2x7 + -8y2 + 2y4 Combine like terms: -2y4 + 2y4 = 0 0 = 7x2 + -2x7 + -8y2 + 2y4 Simplifying 0 = 7x2 + -2x7 + -8y2 + 2y4 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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