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Simplifying (2x + y)(4x + -9y) = 0 Multiply (2x + y) * (4x + -9y) (2x * (4x + -9y) + y(4x + -9y)) = 0 ((4x * 2x + -9y * 2x) + y(4x + -9y)) = 0 Reorder the terms: ((-18xy + 8x2) + y(4x + -9y)) = 0 ((-18xy + 8x2) + y(4x + -9y)) = 0 (-18xy + 8x2 + (4x * y + -9y * y)) = 0 (-18xy + 8x2 + (4xy + -9y2)) = 0 Reorder the terms: (-18xy + 4xy + 8x2 + -9y2) = 0 Combine like terms: -18xy + 4xy = -14xy (-14xy + 8x2 + -9y2) = 0 Solving -14xy + 8x2 + -9y2 = 0 Solving for variable 'x'. Factor a trinomial. (4x + -9y)(2x + y) = 0Subproblem 1
Set the factor '(4x + -9y)' equal to zero and attempt to solve: Simplifying 4x + -9y = 0 Solving 4x + -9y = 0 Move all terms containing x to the left, all other terms to the right. Add '9y' to each side of the equation. 4x + -9y + 9y = 0 + 9y Combine like terms: -9y + 9y = 0 4x + 0 = 0 + 9y 4x = 0 + 9y Remove the zero: 4x = 9y Divide each side by '4'. x = 2.25y Simplifying x = 2.25ySubproblem 2
Set the factor '(2x + y)' equal to zero and attempt to solve: Simplifying 2x + y = 0 Solving 2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 2x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 2x + 0 = 0 + -1y 2x = 0 + -1y Remove the zero: 2x = -1y Divide each side by '2'. x = -0.5y Simplifying x = -0.5ySolution
x = {2.25y, -0.5y}
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