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Simplifying 288x2 + 296xy + -80y2 = 0 Reorder the terms: 296xy + 288x2 + -80y2 = 0 Solving 296xy + 288x2 + -80y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(37xy + 36x2 + -10y2) = 0 Factor a trinomial. 8((9x + -2y)(4x + 5y)) = 0 Ignore the factor 8.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 '(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 = -1.25ySolution
x = {0.2222222222y, -1.25y}
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