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Simplifying 0 = (50x + -80x * y)(80 + -1y(50 + -1x)) Multiply x * y 0 = (50x + -80xy)(80 + -1y(50 + -1x)) 0 = (50x + -80xy)(80 + (50 * -1y + -1x * -1y)) Reorder the terms: 0 = (50x + -80xy)(80 + (1xy + -50y)) 0 = (50x + -80xy)(80 + (1xy + -50y)) Multiply (50x + -80xy) * (80 + 1xy + -50y) 0 = (50x * (80 + 1xy + -50y) + -80xy * (80 + 1xy + -50y)) 0 = ((80 * 50x + 1xy * 50x + -50y * 50x) + -80xy * (80 + 1xy + -50y)) Reorder the terms: 0 = ((4000x + -2500xy + 50x2y) + -80xy * (80 + 1xy + -50y)) 0 = ((4000x + -2500xy + 50x2y) + -80xy * (80 + 1xy + -50y)) 0 = (4000x + -2500xy + 50x2y + (80 * -80xy + 1xy * -80xy + -50y * -80xy)) Reorder the terms: 0 = (4000x + -2500xy + 50x2y + (-6400xy + 4000xy2 + -80x2y2)) 0 = (4000x + -2500xy + 50x2y + (-6400xy + 4000xy2 + -80x2y2)) Reorder the terms: 0 = (4000x + -2500xy + -6400xy + 4000xy2 + 50x2y + -80x2y2) Combine like terms: -2500xy + -6400xy = -8900xy 0 = (4000x + -8900xy + 4000xy2 + 50x2y + -80x2y2) Solving 0 = 4000x + -8900xy + 4000xy2 + 50x2y + -80x2y2 Solving for variable 'x'. Remove the zero: -4000x + 8900xy + -4000xy2 + -50x2y + 80x2y2 = 4000x + -8900xy + 4000xy2 + 50x2y + -80x2y2 + -4000x + 8900xy + -4000xy2 + -50x2y + 80x2y2 Reorder the terms: -4000x + 8900xy + -4000xy2 + -50x2y + 80x2y2 = 4000x + -4000x + -8900xy + 8900xy + 4000xy2 + -4000xy2 + 50x2y + -50x2y + -80x2y2 + 80x2y2 Combine like terms: 4000x + -4000x = 0 -4000x + 8900xy + -4000xy2 + -50x2y + 80x2y2 = 0 + -8900xy + 8900xy + 4000xy2 + -4000xy2 + 50x2y + -50x2y + -80x2y2 + 80x2y2 -4000x + 8900xy + -4000xy2 + -50x2y + 80x2y2 = -8900xy + 8900xy + 4000xy2 + -4000xy2 + 50x2y + -50x2y + -80x2y2 + 80x2y2 Combine like terms: -8900xy + 8900xy = 0 -4000x + 8900xy + -4000xy2 + -50x2y + 80x2y2 = 0 + 4000xy2 + -4000xy2 + 50x2y + -50x2y + -80x2y2 + 80x2y2 -4000x + 8900xy + -4000xy2 + -50x2y + 80x2y2 = 4000xy2 + -4000xy2 + 50x2y + -50x2y + -80x2y2 + 80x2y2 Combine like terms: 4000xy2 + -4000xy2 = 0 -4000x + 8900xy + -4000xy2 + -50x2y + 80x2y2 = 0 + 50x2y + -50x2y + -80x2y2 + 80x2y2 -4000x + 8900xy + -4000xy2 + -50x2y + 80x2y2 = 50x2y + -50x2y + -80x2y2 + 80x2y2 Combine like terms: 50x2y + -50x2y = 0 -4000x + 8900xy + -4000xy2 + -50x2y + 80x2y2 = 0 + -80x2y2 + 80x2y2 -4000x + 8900xy + -4000xy2 + -50x2y + 80x2y2 = -80x2y2 + 80x2y2 Combine like terms: -80x2y2 + 80x2y2 = 0 -4000x + 8900xy + -4000xy2 + -50x2y + 80x2y2 = 0 Factor out the Greatest Common Factor (GCF), '10x'. 10x(-400 + 890y + -400y2 + -5xy + 8xy2) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-400 + 890y + -400y2 + -5xy + 8xy2)' equal to zero and attempt to solve: Simplifying -400 + 890y + -400y2 + -5xy + 8xy2 = 0 Reorder the terms: -400 + -5xy + 8xy2 + 890y + -400y2 = 0 Solving -400 + -5xy + 8xy2 + 890y + -400y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + -5xy + 8xy2 + 890y + 400 + -400y2 = 0 + 400 Reorder the terms: -400 + 400 + -5xy + 8xy2 + 890y + -400y2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -5xy + 8xy2 + 890y + -400y2 = 0 + 400 -5xy + 8xy2 + 890y + -400y2 = 0 + 400 Combine like terms: 0 + 400 = 400 -5xy + 8xy2 + 890y + -400y2 = 400 Add '-890y' to each side of the equation. -5xy + 8xy2 + 890y + -890y + -400y2 = 400 + -890y Combine like terms: 890y + -890y = 0 -5xy + 8xy2 + 0 + -400y2 = 400 + -890y -5xy + 8xy2 + -400y2 = 400 + -890y Add '400y2' to each side of the equation. -5xy + 8xy2 + -400y2 + 400y2 = 400 + -890y + 400y2 Combine like terms: -400y2 + 400y2 = 0 -5xy + 8xy2 + 0 = 400 + -890y + 400y2 -5xy + 8xy2 = 400 + -890y + 400y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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