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Simplifying -108x2 + 204xy + -40y2 = 0 Reorder the terms: 204xy + -108x2 + -40y2 = 0 Solving 204xy + -108x2 + -40y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(51xy + -27x2 + -10y2) = 0 Factor a trinomial. 4((-9x + 2y)(3x + -5y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9x + 2y)' equal to zero and attempt to solve: Simplifying -9x + 2y = 0 Solving -9x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. -9x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 -9x + 0 = 0 + -2y -9x = 0 + -2y Remove the zero: -9x = -2y Divide each side by '-9'. x = 0.2222222222y Simplifying x = 0.2222222222ySubproblem 2
Set the factor '(3x + -5y)' equal to zero and attempt to solve: Simplifying 3x + -5y = 0 Solving 3x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 3x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 3x + 0 = 0 + 5y 3x = 0 + 5y Remove the zero: 3x = 5y Divide each side by '3'. x = 1.666666667y Simplifying x = 1.666666667ySolution
x = {0.2222222222y, 1.666666667y}
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