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Simplifying (2x + -1)(x + -2) = (1 + -2x)(x + 2) Reorder the terms: (-1 + 2x)(x + -2) = (1 + -2x)(x + 2) Reorder the terms: (-1 + 2x)(-2 + x) = (1 + -2x)(x + 2) Multiply (-1 + 2x) * (-2 + x) (-1(-2 + x) + 2x * (-2 + x)) = (1 + -2x)(x + 2) ((-2 * -1 + x * -1) + 2x * (-2 + x)) = (1 + -2x)(x + 2) ((2 + -1x) + 2x * (-2 + x)) = (1 + -2x)(x + 2) (2 + -1x + (-2 * 2x + x * 2x)) = (1 + -2x)(x + 2) (2 + -1x + (-4x + 2x2)) = (1 + -2x)(x + 2) Combine like terms: -1x + -4x = -5x (2 + -5x + 2x2) = (1 + -2x)(x + 2) Reorder the terms: 2 + -5x + 2x2 = (1 + -2x)(2 + x) Multiply (1 + -2x) * (2 + x) 2 + -5x + 2x2 = (1(2 + x) + -2x * (2 + x)) 2 + -5x + 2x2 = ((2 * 1 + x * 1) + -2x * (2 + x)) 2 + -5x + 2x2 = ((2 + 1x) + -2x * (2 + x)) 2 + -5x + 2x2 = (2 + 1x + (2 * -2x + x * -2x)) 2 + -5x + 2x2 = (2 + 1x + (-4x + -2x2)) Combine like terms: 1x + -4x = -3x 2 + -5x + 2x2 = (2 + -3x + -2x2) Add '-2' to each side of the equation. 2 + -5x + -2 + 2x2 = 2 + -3x + -2 + -2x2 Reorder the terms: 2 + -2 + -5x + 2x2 = 2 + -3x + -2 + -2x2 Combine like terms: 2 + -2 = 0 0 + -5x + 2x2 = 2 + -3x + -2 + -2x2 -5x + 2x2 = 2 + -3x + -2 + -2x2 Reorder the terms: -5x + 2x2 = 2 + -2 + -3x + -2x2 Combine like terms: 2 + -2 = 0 -5x + 2x2 = 0 + -3x + -2x2 -5x + 2x2 = -3x + -2x2 Solving -5x + 2x2 = -3x + -2x2 Solving for variable 'x'. Reorder the terms: -5x + 3x + 2x2 + 2x2 = -3x + -2x2 + 3x + 2x2 Combine like terms: -5x + 3x = -2x -2x + 2x2 + 2x2 = -3x + -2x2 + 3x + 2x2 Combine like terms: 2x2 + 2x2 = 4x2 -2x + 4x2 = -3x + -2x2 + 3x + 2x2 Reorder the terms: -2x + 4x2 = -3x + 3x + -2x2 + 2x2 Combine like terms: -3x + 3x = 0 -2x + 4x2 = 0 + -2x2 + 2x2 -2x + 4x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-1 + 2x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Divide each side by '2'. x = 0.5 Simplifying x = 0.5Solution
x = {0, 0.5}
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