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Simplifying nfor((2x2 + 3y2 + -7) * x) * dx + -1((3x2 + 2y2 + -8) * y) * dy = 0 Reorder the terms: fnor((-7 + 2x2 + 3y2) * x) * dx + -1((3x2 + 2y2 + -8) * y) * dy = 0 Reorder the terms for easier multiplication: fnor(x(-7 + 2x2 + 3y2)) * dx + -1((3x2 + 2y2 + -8) * y) * dy = 0 fnor((-7 * x + 2x2 * x + 3y2 * x)) * dx + -1((3x2 + 2y2 + -8) * y) * dy = 0 Reorder the terms: fnor((-7x + 3xy2 + 2x3)) * dx + -1((3x2 + 2y2 + -8) * y) * dy = 0 fnor((-7x + 3xy2 + 2x3)) * dx + -1((3x2 + 2y2 + -8) * y) * dy = 0 Reorder the terms for easier multiplication: fnor * dx(-7x + 3xy2 + 2x3) + -1((3x2 + 2y2 + -8) * y) * dy = 0 Multiply fnor * dx dfnorx(-7x + 3xy2 + 2x3) + -1((3x2 + 2y2 + -8) * y) * dy = 0 (-7x * dfnorx + 3xy2 * dfnorx + 2x3 * dfnorx) + -1((3x2 + 2y2 + -8) * y) * dy = 0 (-7dfnorx2 + 3dfnorx2y2 + 2dfnorx4) + -1((3x2 + 2y2 + -8) * y) * dy = 0 Reorder the terms: -7dfnorx2 + 3dfnorx2y2 + 2dfnorx4 + -1((-8 + 3x2 + 2y2) * y) * dy = 0 Reorder the terms for easier multiplication: -7dfnorx2 + 3dfnorx2y2 + 2dfnorx4 + -1(y(-8 + 3x2 + 2y2)) * dy = 0 -7dfnorx2 + 3dfnorx2y2 + 2dfnorx4 + -1((-8 * y + 3x2 * y + 2y2 * y)) * dy = 0 Reorder the terms: -7dfnorx2 + 3dfnorx2y2 + 2dfnorx4 + -1((3x2y + -8y + 2y3)) * dy = 0 -7dfnorx2 + 3dfnorx2y2 + 2dfnorx4 + -1((3x2y + -8y + 2y3)) * dy = 0 Reorder the terms for easier multiplication: -7dfnorx2 + 3dfnorx2y2 + 2dfnorx4 + -1dy(3x2y + -8y + 2y3) = 0 -7dfnorx2 + 3dfnorx2y2 + 2dfnorx4 + (3x2y * -1dy + -8y * -1dy + 2y3 * -1dy) = 0 -7dfnorx2 + 3dfnorx2y2 + 2dfnorx4 + (-3dx2y2 + 8dy2 + -2dy4) = 0 Solving -7dfnorx2 + 3dfnorx2y2 + 2dfnorx4 + -3dx2y2 + 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(-7fnorx2 + 3fnorx2y2 + 2fnorx4 + -3x2y2 + 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 '(-7fnorx2 + 3fnorx2y2 + 2fnorx4 + -3x2y2 + 8y2 + -2y4)' equal to zero and attempt to solve: Simplifying -7fnorx2 + 3fnorx2y2 + 2fnorx4 + -3x2y2 + 8y2 + -2y4 = 0 Solving -7fnorx2 + 3fnorx2y2 + 2fnorx4 + -3x2y2 + 8y2 + -2y4 = 0 Move all terms containing d to the left, all other terms to the right. Add '7fnorx2' to each side of the equation. -7fnorx2 + 3fnorx2y2 + 2fnorx4 + -3x2y2 + 8y2 + 7fnorx2 + -2y4 = 0 + 7fnorx2 Reorder the terms: -7fnorx2 + 7fnorx2 + 3fnorx2y2 + 2fnorx4 + -3x2y2 + 8y2 + -2y4 = 0 + 7fnorx2 Combine like terms: -7fnorx2 + 7fnorx2 = 0 0 + 3fnorx2y2 + 2fnorx4 + -3x2y2 + 8y2 + -2y4 = 0 + 7fnorx2 3fnorx2y2 + 2fnorx4 + -3x2y2 + 8y2 + -2y4 = 0 + 7fnorx2 Remove the zero: 3fnorx2y2 + 2fnorx4 + -3x2y2 + 8y2 + -2y4 = 7fnorx2 Add '-3fnorx2y2' to each side of the equation. 3fnorx2y2 + 2fnorx4 + -3x2y2 + 8y2 + -3fnorx2y2 + -2y4 = 7fnorx2 + -3fnorx2y2 Reorder the terms: 3fnorx2y2 + -3fnorx2y2 + 2fnorx4 + -3x2y2 + 8y2 + -2y4 = 7fnorx2 + -3fnorx2y2 Combine like terms: 3fnorx2y2 + -3fnorx2y2 = 0 0 + 2fnorx4 + -3x2y2 + 8y2 + -2y4 = 7fnorx2 + -3fnorx2y2 2fnorx4 + -3x2y2 + 8y2 + -2y4 = 7fnorx2 + -3fnorx2y2 Add '-2fnorx4' to each side of the equation. 2fnorx4 + -3x2y2 + 8y2 + -2fnorx4 + -2y4 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 Reorder the terms: 2fnorx4 + -2fnorx4 + -3x2y2 + 8y2 + -2y4 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 Combine like terms: 2fnorx4 + -2fnorx4 = 0 0 + -3x2y2 + 8y2 + -2y4 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 -3x2y2 + 8y2 + -2y4 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 Add '3x2y2' to each side of the equation. -3x2y2 + 8y2 + 3x2y2 + -2y4 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 + 3x2y2 Reorder the terms: -3x2y2 + 3x2y2 + 8y2 + -2y4 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 + 3x2y2 Combine like terms: -3x2y2 + 3x2y2 = 0 0 + 8y2 + -2y4 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 + 3x2y2 8y2 + -2y4 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 + 3x2y2 Add '-8y2' to each side of the equation. 8y2 + -8y2 + -2y4 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 + 3x2y2 + -8y2 Combine like terms: 8y2 + -8y2 = 0 0 + -2y4 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 + 3x2y2 + -8y2 -2y4 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 + 3x2y2 + -8y2 Add '2y4' to each side of the equation. -2y4 + 2y4 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 + 3x2y2 + -8y2 + 2y4 Combine like terms: -2y4 + 2y4 = 0 0 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 + 3x2y2 + -8y2 + 2y4 Simplifying 0 = 7fnorx2 + -3fnorx2y2 + -2fnorx4 + 3x2y2 + -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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