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Simplifying 81x2 + 108xy + 36y2 = 0 Reorder the terms: 108xy + 81x2 + 36y2 = 0 Solving 108xy + 81x2 + 36y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(12xy + 9x2 + 4y2) = 0 Factor a trinomial. 9((3x + 2y)(3x + 2y)) = 0 Ignore the factor 9.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 '(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 = -0.6666666667ySolution
x = {-0.6666666667y, -0.6666666667y}
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