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Simplifying 36x2 + 12xy + -24y2 = 0 Reorder the terms: 12xy + 36x2 + -24y2 = 0 Solving 12xy + 36x2 + -24y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(xy + 3x2 + -2y2) = 0 Factor a trinomial. 12((3x + -2y)(x + y)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(3x + -2y)' equal to zero and attempt to solve: Simplifying 3x + -2y = 0 Solving 3x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 3x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 3x + 0 = 0 + 2y 3x = 0 + 2y Remove the zero: 3x = 2y Divide each side by '3'. x = 0.6666666667y Simplifying x = 0.6666666667ySubproblem 2
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 = {0.6666666667y, -1y}
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