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