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Simplifying 9x2 + 12xy + 3y2 = 0 Reorder the terms: 12xy + 9x2 + 3y2 = 0 Solving 12xy + 9x2 + 3y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4xy + 3x2 + y2) = 0 Factor a trinomial. 3((3x + y)(x + y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3x + y)' equal to zero and attempt to solve: Simplifying 3x + y = 0 Solving 3x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 3x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 3x + 0 = 0 + -1y 3x = 0 + -1y Remove the zero: 3x = -1y Divide each side by '3'. x = -0.3333333333y Simplifying x = -0.3333333333ySubproblem 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 = {-0.3333333333y, -1y}
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