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Simplifying 45x2 + 48xy + -45y2 = 0 Reorder the terms: 48xy + 45x2 + -45y2 = 0 Solving 48xy + 45x2 + -45y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(16xy + 15x2 + -15y2) = 0 Factor a trinomial. 3((5x + -3y)(3x + 5y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5x + -3y)' equal to zero and attempt to solve: Simplifying 5x + -3y = 0 Solving 5x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 5x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 5x + 0 = 0 + 3y 5x = 0 + 3y Remove the zero: 5x = 3y Divide each side by '5'. x = 0.6y Simplifying x = 0.6ySubproblem 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 = {0.6y, -1.666666667y}
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