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Simplifying 6x2 + 8xy + -14y2 = 0 Reorder the terms: 8xy + 6x2 + -14y2 = 0 Solving 8xy + 6x2 + -14y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4xy + 3x2 + -7y2) = 0 Factor a trinomial. 2((x + -1y)(3x + 7y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. x + -1y + y = 0 + y Combine like terms: -1y + y = 0 x + 0 = 0 + y x = 0 + y Remove the zero: x = y Simplifying x = ySubproblem 2
Set the factor '(3x + 7y)' equal to zero and attempt to solve: Simplifying 3x + 7y = 0 Solving 3x + 7y = 0 Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. 3x + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 3x + 0 = 0 + -7y 3x = 0 + -7y Remove the zero: 3x = -7y Divide each side by '3'. x = -2.333333333y Simplifying x = -2.333333333ySolution
x = {y, -2.333333333y}
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