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Simplifying 32x2 + 120xy + -108y2 = 0 Reorder the terms: 120xy + 32x2 + -108y2 = 0 Solving 120xy + 32x2 + -108y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(30xy + 8x2 + -27y2) = 0 Factor a trinomial. 4((4x + -3y)(2x + 9y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4x + -3y)' equal to zero and attempt to solve: Simplifying 4x + -3y = 0 Solving 4x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 4x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 4x + 0 = 0 + 3y 4x = 0 + 3y Remove the zero: 4x = 3y Divide each side by '4'. x = 0.75y Simplifying x = 0.75ySubproblem 2
Set the factor '(2x + 9y)' equal to zero and attempt to solve: Simplifying 2x + 9y = 0 Solving 2x + 9y = 0 Move all terms containing x to the left, all other terms to the right. Add '-9y' to each side of the equation. 2x + 9y + -9y = 0 + -9y Combine like terms: 9y + -9y = 0 2x + 0 = 0 + -9y 2x = 0 + -9y Remove the zero: 2x = -9y Divide each side by '2'. x = -4.5y Simplifying x = -4.5ySolution
x = {0.75y, -4.5y}
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