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Simplifying -24x2 + 90xy + -75y2 = 0 Reorder the terms: 90xy + -24x2 + -75y2 = 0 Solving 90xy + -24x2 + -75y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(30xy + -8x2 + -25y2) = 0 Factor a trinomial. 3((-4x + 5y)(2x + -5y)) = 0 Ignore the factor 3.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 '(2x + -5y)' equal to zero and attempt to solve: Simplifying 2x + -5y = 0 Solving 2x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 2x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 2x + 0 = 0 + 5y 2x = 0 + 5y Remove the zero: 2x = 5y Divide each side by '2'. x = 2.5y Simplifying x = 2.5ySolution
x = {1.25y, 2.5y}
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