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Simplifying 12x2 + 46xy + -8y2 = 0 Reorder the terms: 46xy + 12x2 + -8y2 = 0 Solving 46xy + 12x2 + -8y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(23xy + 6x2 + -4y2) = 0 Factor a trinomial. 2((6x + -1y)(x + 4y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6x + -1y)' equal to zero and attempt to solve: Simplifying 6x + -1y = 0 Solving 6x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 6x + -1y + y = 0 + y Combine like terms: -1y + y = 0 6x + 0 = 0 + y 6x = 0 + y Remove the zero: 6x = y Divide each side by '6'. x = 0.1666666667y Simplifying x = 0.1666666667ySubproblem 2
Set the factor '(x + 4y)' equal to zero and attempt to solve: Simplifying x + 4y = 0 Solving x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 x + 0 = 0 + -4y x = 0 + -4y Remove the zero: x = -4y Simplifying x = -4ySolution
x = {0.1666666667y, -4y}
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