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Simplifying (x + 2)(x + 2)(x + 2) = x3 + 2 Reorder the terms: (2 + x)(x + 2)(x + 2) = x3 + 2 Reorder the terms: (2 + x)(2 + x)(x + 2) = x3 + 2 Reorder the terms: (2 + x)(2 + x)(2 + x) = x3 + 2 Multiply (2 + x) * (2 + x) (2(2 + x) + x(2 + x))(2 + x) = x3 + 2 ((2 * 2 + x * 2) + x(2 + x))(2 + x) = x3 + 2 ((4 + 2x) + x(2 + x))(2 + x) = x3 + 2 (4 + 2x + (2 * x + x * x))(2 + x) = x3 + 2 (4 + 2x + (2x + x2))(2 + x) = x3 + 2 Combine like terms: 2x + 2x = 4x (4 + 4x + x2)(2 + x) = x3 + 2 Multiply (4 + 4x + x2) * (2 + x) (4(2 + x) + 4x * (2 + x) + x2(2 + x)) = x3 + 2 ((2 * 4 + x * 4) + 4x * (2 + x) + x2(2 + x)) = x3 + 2 ((8 + 4x) + 4x * (2 + x) + x2(2 + x)) = x3 + 2 (8 + 4x + (2 * 4x + x * 4x) + x2(2 + x)) = x3 + 2 (8 + 4x + (8x + 4x2) + x2(2 + x)) = x3 + 2 (8 + 4x + 8x + 4x2 + (2 * x2 + x * x2)) = x3 + 2 (8 + 4x + 8x + 4x2 + (2x2 + x3)) = x3 + 2 Combine like terms: 4x + 8x = 12x (8 + 12x + 4x2 + 2x2 + x3) = x3 + 2 Combine like terms: 4x2 + 2x2 = 6x2 (8 + 12x + 6x2 + x3) = x3 + 2 Reorder the terms: 8 + 12x + 6x2 + x3 = 2 + x3 Add '-1x3' to each side of the equation. 8 + 12x + 6x2 + x3 + -1x3 = 2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 8 + 12x + 6x2 + 0 = 2 + x3 + -1x3 8 + 12x + 6x2 = 2 + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 8 + 12x + 6x2 = 2 + 0 8 + 12x + 6x2 = 2 Solving 8 + 12x + 6x2 = 2 Solving for variable 'x'. Reorder the terms: 8 + -2 + 12x + 6x2 = 2 + -2 Combine like terms: 8 + -2 = 6 6 + 12x + 6x2 = 2 + -2 Combine like terms: 2 + -2 = 0 6 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(1 + 2x + x2) = 0 Factor a trinomial. 6((1 + x)(1 + x)) = 0 Ignore the factor 6.Subproblem 1
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 = -1Subproblem 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 = {-1, -1}
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