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Simplifying (2x + -1)(2x + -1) = (x + 1)(x + 1) Reorder the terms: (-1 + 2x)(2x + -1) = (x + 1)(x + 1) Reorder the terms: (-1 + 2x)(-1 + 2x) = (x + 1)(x + 1) Multiply (-1 + 2x) * (-1 + 2x) (-1(-1 + 2x) + 2x * (-1 + 2x)) = (x + 1)(x + 1) ((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = (x + 1)(x + 1) ((1 + -2x) + 2x * (-1 + 2x)) = (x + 1)(x + 1) (1 + -2x + (-1 * 2x + 2x * 2x)) = (x + 1)(x + 1) (1 + -2x + (-2x + 4x2)) = (x + 1)(x + 1) Combine like terms: -2x + -2x = -4x (1 + -4x + 4x2) = (x + 1)(x + 1) Reorder the terms: 1 + -4x + 4x2 = (1 + x)(x + 1) Reorder the terms: 1 + -4x + 4x2 = (1 + x)(1 + x) Multiply (1 + x) * (1 + x) 1 + -4x + 4x2 = (1(1 + x) + x(1 + x)) 1 + -4x + 4x2 = ((1 * 1 + x * 1) + x(1 + x)) 1 + -4x + 4x2 = ((1 + 1x) + x(1 + x)) 1 + -4x + 4x2 = (1 + 1x + (1 * x + x * x)) 1 + -4x + 4x2 = (1 + 1x + (1x + x2)) Combine like terms: 1x + 1x = 2x 1 + -4x + 4x2 = (1 + 2x + x2) Add '-1' to each side of the equation. 1 + -4x + -1 + 4x2 = 1 + 2x + -1 + x2 Reorder the terms: 1 + -1 + -4x + 4x2 = 1 + 2x + -1 + x2 Combine like terms: 1 + -1 = 0 0 + -4x + 4x2 = 1 + 2x + -1 + x2 -4x + 4x2 = 1 + 2x + -1 + x2 Reorder the terms: -4x + 4x2 = 1 + -1 + 2x + x2 Combine like terms: 1 + -1 = 0 -4x + 4x2 = 0 + 2x + x2 -4x + 4x2 = 2x + x2 Solving -4x + 4x2 = 2x + x2 Solving for variable 'x'. Reorder the terms: -4x + -2x + 4x2 + -1x2 = 2x + x2 + -2x + -1x2 Combine like terms: -4x + -2x = -6x -6x + 4x2 + -1x2 = 2x + x2 + -2x + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 -6x + 3x2 = 2x + x2 + -2x + -1x2 Reorder the terms: -6x + 3x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 -6x + 3x2 = 0 + x2 + -1x2 -6x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-2 + x) = 0 Ignore the factor 3.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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Solution
x = {0, 2}
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