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Simplifying ((x + 2)(x + 2)(x + 2)) + -1(x * x * x) = 152 Reorder the terms: ((2 + x)(x + 2)(x + 2)) + -1(x * x * x) = 152 Reorder the terms: ((2 + x)(2 + x)(x + 2)) + -1(x * x * x) = 152 Reorder the terms: ((2 + x)(2 + x)(2 + x)) + -1(x * x * x) = 152 Multiply (2 + x) * (2 + x) ((2(2 + x) + x(2 + x))(2 + x)) + -1(x * x * x) = 152 (((2 * 2 + x * 2) + x(2 + x))(2 + x)) + -1(x * x * x) = 152 (((4 + 2x) + x(2 + x))(2 + x)) + -1(x * x * x) = 152 ((4 + 2x + (2 * x + x * x))(2 + x)) + -1(x * x * x) = 152 ((4 + 2x + (2x + x2))(2 + x)) + -1(x * x * x) = 152 Combine like terms: 2x + 2x = 4x ((4 + 4x + x2)(2 + x)) + -1(x * x * x) = 152 Multiply (4 + 4x + x2) * (2 + x) ((4(2 + x) + 4x * (2 + x) + x2(2 + x))) + -1(x * x * x) = 152 (((2 * 4 + x * 4) + 4x * (2 + x) + x2(2 + x))) + -1(x * x * x) = 152 (((8 + 4x) + 4x * (2 + x) + x2(2 + x))) + -1(x * x * x) = 152 ((8 + 4x + (2 * 4x + x * 4x) + x2(2 + x))) + -1(x * x * x) = 152 ((8 + 4x + (8x + 4x2) + x2(2 + x))) + -1(x * x * x) = 152 ((8 + 4x + 8x + 4x2 + (2 * x2 + x * x2))) + -1(x * x * x) = 152 ((8 + 4x + 8x + 4x2 + (2x2 + x3))) + -1(x * x * x) = 152 Combine like terms: 4x + 8x = 12x ((8 + 12x + 4x2 + 2x2 + x3)) + -1(x * x * x) = 152 Combine like terms: 4x2 + 2x2 = 6x2 ((8 + 12x + 6x2 + x3)) + -1(x * x * x) = 152 (8 + 12x + 6x2 + x3) + -1(x * x * x) = 152 Remove parenthesis around (8 + 12x + 6x2 + x3) 8 + 12x + 6x2 + x3 + -1(x * x * x) = 152 Multiply x * x 8 + 12x + 6x2 + x3 + -1(x2 * x) = 152 Multiply x2 * x 8 + 12x + 6x2 + x3 + -1(x3) = 152 Combine like terms: x3 + -1x3 = 0 8 + 12x + 6x2 + 0 = 152 8 + 12x + 6x2 = 152 Solving 8 + 12x + 6x2 = 152 Solving for variable 'x'. Reorder the terms: 8 + -152 + 12x + 6x2 = 152 + -152 Combine like terms: 8 + -152 = -144 -144 + 12x + 6x2 = 152 + -152 Combine like terms: 152 + -152 = 0 -144 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-24 + 2x + x2) = 0 Factor a trinomial. 6((-6 + -1x)(4 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-6, 4}
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