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