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Simplifying 96x2 + 144xy + 54y2 = 0 Reorder the terms: 144xy + 96x2 + 54y2 = 0 Solving 144xy + 96x2 + 54y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(24xy + 16x2 + 9y2) = 0 Factor a trinomial. 6((4x + 3y)(4x + 3y)) = 0 Ignore the factor 6.Subproblem 1
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 = -0.75ySubproblem 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 = {-0.75y, -0.75y}
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