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Simplifying 18x2 + 12xy + -16y2 = 0 Reorder the terms: 12xy + 18x2 + -16y2 = 0 Solving 12xy + 18x2 + -16y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6xy + 9x2 + -8y2) = 0 Factor a trinomial. 2((3x + -2y)(3x + 4y)) = 0 Ignore the factor 2.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 + 4y)' equal to zero and attempt to solve: Simplifying 3x + 4y = 0 Solving 3x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 3x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 3x + 0 = 0 + -4y 3x = 0 + -4y Remove the zero: 3x = -4y Divide each side by '3'. x = -1.333333333y Simplifying x = -1.333333333ySolution
x = {0.6666666667y, -1.333333333y}
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