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Simplifying 8x2 + -34xy + -30y2 = 0 Reorder the terms: -34xy + 8x2 + -30y2 = 0 Solving -34xy + 8x2 + -30y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-17xy + 4x2 + -15y2) = 0 Factor a trinomial. 2((x + -5y)(4x + 3y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(x + -5y)' equal to zero and attempt to solve: Simplifying x + -5y = 0 Solving x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 x + 0 = 0 + 5y x = 0 + 5y Remove the zero: x = 5y Simplifying x = 5ySubproblem 2
Set the factor '(4x + 3y)' equal to zero and attempt to solve: Simplifying 4x + 3y = 0 Solving 4x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 4x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 4x + 0 = 0 + -3y 4x = 0 + -3y Remove the zero: 4x = -3y Divide each side by '4'. x = -0.75y Simplifying x = -0.75ySolution
x = {5y, -0.75y}
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