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Simplifying (x + -1)(x + -1) = 2x2 + 4x + 6 Reorder the terms: (-1 + x)(x + -1) = 2x2 + 4x + 6 Reorder the terms: (-1 + x)(-1 + x) = 2x2 + 4x + 6 Multiply (-1 + x) * (-1 + x) (-1(-1 + x) + x(-1 + x)) = 2x2 + 4x + 6 ((-1 * -1 + x * -1) + x(-1 + x)) = 2x2 + 4x + 6 ((1 + -1x) + x(-1 + x)) = 2x2 + 4x + 6 (1 + -1x + (-1 * x + x * x)) = 2x2 + 4x + 6 (1 + -1x + (-1x + x2)) = 2x2 + 4x + 6 Combine like terms: -1x + -1x = -2x (1 + -2x + x2) = 2x2 + 4x + 6 Reorder the terms: 1 + -2x + x2 = 6 + 4x + 2x2 Solving 1 + -2x + x2 = 6 + 4x + 2x2 Solving for variable 'x'. Reorder the terms: 1 + -6 + -2x + -4x + x2 + -2x2 = 6 + 4x + 2x2 + -6 + -4x + -2x2 Combine like terms: 1 + -6 = -5 -5 + -2x + -4x + x2 + -2x2 = 6 + 4x + 2x2 + -6 + -4x + -2x2 Combine like terms: -2x + -4x = -6x -5 + -6x + x2 + -2x2 = 6 + 4x + 2x2 + -6 + -4x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -5 + -6x + -1x2 = 6 + 4x + 2x2 + -6 + -4x + -2x2 Reorder the terms: -5 + -6x + -1x2 = 6 + -6 + 4x + -4x + 2x2 + -2x2 Combine like terms: 6 + -6 = 0 -5 + -6x + -1x2 = 0 + 4x + -4x + 2x2 + -2x2 -5 + -6x + -1x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 -5 + -6x + -1x2 = 0 + 2x2 + -2x2 -5 + -6x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -5 + -6x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 6x + x2) = 0 Factor a trinomial. -1((5 + x)(1 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 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 = {-5, -1}
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