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Simplifying (2x2 + 3y2 + -7) * x * dx + -1(3x2 + 2y2 + -8) * dy = 0 Reorder the terms: (-7 + 2x2 + 3y2) * x * dx + -1(3x2 + 2y2 + -8) * dy = 0 Reorder the terms for easier multiplication: x * dx(-7 + 2x2 + 3y2) + -1(3x2 + 2y2 + -8) * dy = 0 Multiply x * dx dx2(-7 + 2x2 + 3y2) + -1(3x2 + 2y2 + -8) * dy = 0 (-7 * dx2 + 2x2 * dx2 + 3y2 * dx2) + -1(3x2 + 2y2 + -8) * dy = 0 Reorder the terms: (-7dx2 + 3dx2y2 + 2dx4) + -1(3x2 + 2y2 + -8) * dy = 0 (-7dx2 + 3dx2y2 + 2dx4) + -1(3x2 + 2y2 + -8) * dy = 0 Reorder the terms: -7dx2 + 3dx2y2 + 2dx4 + -1(-8 + 3x2 + 2y2) * dy = 0 Reorder the terms for easier multiplication: -7dx2 + 3dx2y2 + 2dx4 + -1dy(-8 + 3x2 + 2y2) = 0 -7dx2 + 3dx2y2 + 2dx4 + (-8 * -1dy + 3x2 * -1dy + 2y2 * -1dy) = 0 Reorder the terms: -7dx2 + 3dx2y2 + 2dx4 + (-3dx2y + 8dy + -2dy3) = 0 -7dx2 + 3dx2y2 + 2dx4 + (-3dx2y + 8dy + -2dy3) = 0 Reorder the terms: -7dx2 + -3dx2y + 3dx2y2 + 2dx4 + 8dy + -2dy3 = 0 Solving -7dx2 + -3dx2y + 3dx2y2 + 2dx4 + 8dy + -2dy3 = 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 + -3x2y + 3x2y2 + 2x4 + 8y + -2y3) = 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 + -3x2y + 3x2y2 + 2x4 + 8y + -2y3)' equal to zero and attempt to solve: Simplifying -7x2 + -3x2y + 3x2y2 + 2x4 + 8y + -2y3 = 0 Solving -7x2 + -3x2y + 3x2y2 + 2x4 + 8y + -2y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '7x2' to each side of the equation. -7x2 + -3x2y + 3x2y2 + 2x4 + 8y + 7x2 + -2y3 = 0 + 7x2 Reorder the terms: -7x2 + 7x2 + -3x2y + 3x2y2 + 2x4 + 8y + -2y3 = 0 + 7x2 Combine like terms: -7x2 + 7x2 = 0 0 + -3x2y + 3x2y2 + 2x4 + 8y + -2y3 = 0 + 7x2 -3x2y + 3x2y2 + 2x4 + 8y + -2y3 = 0 + 7x2 Remove the zero: -3x2y + 3x2y2 + 2x4 + 8y + -2y3 = 7x2 Add '3x2y' to each side of the equation. -3x2y + 3x2y2 + 2x4 + 8y + 3x2y + -2y3 = 7x2 + 3x2y Reorder the terms: -3x2y + 3x2y + 3x2y2 + 2x4 + 8y + -2y3 = 7x2 + 3x2y Combine like terms: -3x2y + 3x2y = 0 0 + 3x2y2 + 2x4 + 8y + -2y3 = 7x2 + 3x2y 3x2y2 + 2x4 + 8y + -2y3 = 7x2 + 3x2y Add '-3x2y2' to each side of the equation. 3x2y2 + 2x4 + 8y + -3x2y2 + -2y3 = 7x2 + 3x2y + -3x2y2 Reorder the terms: 3x2y2 + -3x2y2 + 2x4 + 8y + -2y3 = 7x2 + 3x2y + -3x2y2 Combine like terms: 3x2y2 + -3x2y2 = 0 0 + 2x4 + 8y + -2y3 = 7x2 + 3x2y + -3x2y2 2x4 + 8y + -2y3 = 7x2 + 3x2y + -3x2y2 Add '-2x4' to each side of the equation. 2x4 + 8y + -2x4 + -2y3 = 7x2 + 3x2y + -3x2y2 + -2x4 Reorder the terms: 2x4 + -2x4 + 8y + -2y3 = 7x2 + 3x2y + -3x2y2 + -2x4 Combine like terms: 2x4 + -2x4 = 0 0 + 8y + -2y3 = 7x2 + 3x2y + -3x2y2 + -2x4 8y + -2y3 = 7x2 + 3x2y + -3x2y2 + -2x4 Add '-8y' to each side of the equation. 8y + -8y + -2y3 = 7x2 + 3x2y + -3x2y2 + -2x4 + -8y Combine like terms: 8y + -8y = 0 0 + -2y3 = 7x2 + 3x2y + -3x2y2 + -2x4 + -8y -2y3 = 7x2 + 3x2y + -3x2y2 + -2x4 + -8y Add '2y3' to each side of the equation. -2y3 + 2y3 = 7x2 + 3x2y + -3x2y2 + -2x4 + -8y + 2y3 Combine like terms: -2y3 + 2y3 = 0 0 = 7x2 + 3x2y + -3x2y2 + -2x4 + -8y + 2y3 Simplifying 0 = 7x2 + 3x2y + -3x2y2 + -2x4 + -8y + 2y3 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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