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Simplifying 96x2 + 300xy + -126y2 = 0 Reorder the terms: 300xy + 96x2 + -126y2 = 0 Solving 300xy + 96x2 + -126y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(50xy + 16x2 + -21y2) = 0 Factor a trinomial. 6((8x + -3y)(2x + 7y)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(8x + -3y)' equal to zero and attempt to solve: Simplifying 8x + -3y = 0 Solving 8x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 8x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 8x + 0 = 0 + 3y 8x = 0 + 3y Remove the zero: 8x = 3y Divide each side by '8'. x = 0.375y Simplifying x = 0.375ySubproblem 2
Set the factor '(2x + 7y)' equal to zero and attempt to solve: Simplifying 2x + 7y = 0 Solving 2x + 7y = 0 Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. 2x + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 2x + 0 = 0 + -7y 2x = 0 + -7y Remove the zero: 2x = -7y Divide each side by '2'. x = -3.5y Simplifying x = -3.5ySolution
x = {0.375y, -3.5y}
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