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Simplifying 12x2 + 2xy + -10y2 = 0 Reorder the terms: 2xy + 12x2 + -10y2 = 0 Solving 2xy + 12x2 + -10y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(xy + 6x2 + -5y2) = 0 Factor a trinomial. 2((6x + -5y)(x + y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6x + -5y)' equal to zero and attempt to solve: Simplifying 6x + -5y = 0 Solving 6x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 6x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 6x + 0 = 0 + 5y 6x = 0 + 5y Remove the zero: 6x = 5y Divide each side by '6'. x = 0.8333333333y Simplifying x = 0.8333333333ySubproblem 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 = {0.8333333333y, -1y}
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