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Simplifying 48x2 + 4xy + -80y2 = 0 Reorder the terms: 4xy + 48x2 + -80y2 = 0 Solving 4xy + 48x2 + -80y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(xy + 12x2 + -20y2) = 0 Factor a trinomial. 4((4x + -5y)(3x + 4y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4x + -5y)' equal to zero and attempt to solve: Simplifying 4x + -5y = 0 Solving 4x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 4x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 4x + 0 = 0 + 5y 4x = 0 + 5y Remove the zero: 4x = 5y Divide each side by '4'. x = 1.25y Simplifying x = 1.25ySubproblem 2
Set the factor '(3x + 4y)' equal to zero and attempt to solve: Simplifying 3x + 4y = 0 Solving 3x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 3x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 3x + 0 = 0 + -4y 3x = 0 + -4y Remove the zero: 3x = -4y Divide each side by '3'. x = -1.333333333y Simplifying x = -1.333333333ySolution
x = {1.25y, -1.333333333y}
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