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Simplifying 6x2 + -9xy + -81y2 = 0 Reorder the terms: -9xy + 6x2 + -81y2 = 0 Solving -9xy + 6x2 + -81y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3xy + 2x2 + -27y2) = 0 Factor a trinomial. 3((2x + -9y)(x + 3y)) = 0 Ignore the factor 3.Subproblem 1
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 = 4.5ySubproblem 2
Set the factor '(x + 3y)' equal to zero and attempt to solve: Simplifying x + 3y = 0 Solving x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 x + 0 = 0 + -3y x = 0 + -3y Remove the zero: x = -3y Simplifying x = -3ySolution
x = {4.5y, -3y}
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