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Simplifying 160x2 + 24xy + -16y2 = 0 Reorder the terms: 24xy + 160x2 + -16y2 = 0 Solving 24xy + 160x2 + -16y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(3xy + 20x2 + -2y2) = 0 Factor a trinomial. 8((4x + -1y)(5x + 2y)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(4x + -1y)' equal to zero and attempt to solve: Simplifying 4x + -1y = 0 Solving 4x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 4x + -1y + y = 0 + y Combine like terms: -1y + y = 0 4x + 0 = 0 + y 4x = 0 + y Remove the zero: 4x = y Divide each side by '4'. x = 0.25y Simplifying x = 0.25ySubproblem 2
Set the factor '(5x + 2y)' equal to zero and attempt to solve: Simplifying 5x + 2y = 0 Solving 5x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 5x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 5x + 0 = 0 + -2y 5x = 0 + -2y Remove the zero: 5x = -2y Divide each side by '5'. x = -0.4y Simplifying x = -0.4ySolution
x = {0.25y, -0.4y}
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