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Simplifying 25x2 + 240xy + -100y2 = 0 Reorder the terms: 240xy + 25x2 + -100y2 = 0 Solving 240xy + 25x2 + -100y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(48xy + 5x2 + -20y2) = 0 Factor a trinomial. 5((5x + -2y)(x + 10y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5x + -2y)' equal to zero and attempt to solve: Simplifying 5x + -2y = 0 Solving 5x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 5x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 5x + 0 = 0 + 2y 5x = 0 + 2y Remove the zero: 5x = 2y Divide each side by '5'. x = 0.4y Simplifying x = 0.4ySubproblem 2
Set the factor '(x + 10y)' equal to zero and attempt to solve: Simplifying x + 10y = 0 Solving x + 10y = 0 Move all terms containing x to the left, all other terms to the right. Add '-10y' to each side of the equation. x + 10y + -10y = 0 + -10y Combine like terms: 10y + -10y = 0 x + 0 = 0 + -10y x = 0 + -10y Remove the zero: x = -10y Simplifying x = -10ySolution
x = {0.4y, -10y}
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