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Simplifying 125x2 + -200xy + 80y2 = 0 Reorder the terms: -200xy + 125x2 + 80y2 = 0 Solving -200xy + 125x2 + 80y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-40xy + 25x2 + 16y2) = 0 Factor a trinomial. 5((5x + -4y)(5x + -4y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5x + -4y)' equal to zero and attempt to solve: Simplifying 5x + -4y = 0 Solving 5x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. 5x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 5x + 0 = 0 + 4y 5x = 0 + 4y Remove the zero: 5x = 4y Divide each side by '5'. x = 0.8y Simplifying x = 0.8ySubproblem 2
Set the factor '(5x + -4y)' equal to zero and attempt to solve: Simplifying 5x + -4y = 0 Solving 5x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. 5x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 5x + 0 = 0 + 4y 5x = 0 + 4y Remove the zero: 5x = 4y Divide each side by '5'. x = 0.8y Simplifying x = 0.8ySolution
x = {0.8y, 0.8y}
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