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Simplifying 8x2y + 9xy2 + y3 = 0 Reorder the terms: 9xy2 + 8x2y + y3 = 0 Solving 9xy2 + 8x2y + y3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'y'. y(9xy + 8x2 + y2) = 0 Factor a trinomial. y((8x + y)(x + y)) = 0Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y = 0 + -1y Remove the zero: 0 = -1y Simplifying 0 = -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(8x + y)' equal to zero and attempt to solve: Simplifying 8x + y = 0 Solving 8x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 8x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 8x + 0 = 0 + -1y 8x = 0 + -1y Remove the zero: 8x = -1y Divide each side by '8'. x = -0.125y Simplifying x = -0.125ySubproblem 3
Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1ySolution
x = {-0.125y, -1y}
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