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Simplifying -6x + -2 = (3x + 1)(3x + 1) Reorder the terms: -2 + -6x = (3x + 1)(3x + 1) Reorder the terms: -2 + -6x = (1 + 3x)(3x + 1) Reorder the terms: -2 + -6x = (1 + 3x)(1 + 3x) Multiply (1 + 3x) * (1 + 3x) -2 + -6x = (1(1 + 3x) + 3x * (1 + 3x)) -2 + -6x = ((1 * 1 + 3x * 1) + 3x * (1 + 3x)) -2 + -6x = ((1 + 3x) + 3x * (1 + 3x)) -2 + -6x = (1 + 3x + (1 * 3x + 3x * 3x)) -2 + -6x = (1 + 3x + (3x + 9x2)) Combine like terms: 3x + 3x = 6x -2 + -6x = (1 + 6x + 9x2) Solving -2 + -6x = 1 + 6x + 9x2 Solving for variable 'x'. Reorder the terms: -2 + -1 + -6x + -6x + -9x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2 Combine like terms: -2 + -1 = -3 -3 + -6x + -6x + -9x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2 Combine like terms: -6x + -6x = -12x -3 + -12x + -9x2 = 1 + 6x + 9x2 + -1 + -6x + -9x2 Reorder the terms: -3 + -12x + -9x2 = 1 + -1 + 6x + -6x + 9x2 + -9x2 Combine like terms: 1 + -1 = 0 -3 + -12x + -9x2 = 0 + 6x + -6x + 9x2 + -9x2 -3 + -12x + -9x2 = 6x + -6x + 9x2 + -9x2 Combine like terms: 6x + -6x = 0 -3 + -12x + -9x2 = 0 + 9x2 + -9x2 -3 + -12x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -3 + -12x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(1 + 4x + 3x2) = 0 Factor a trinomial. -3((1 + x)(1 + 3x)) = 0 Ignore the factor -3.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 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-1, -0.3333333333}
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