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Simplifying 2 = 3x2 + 12x + 11 Reorder the terms: 2 = 11 + 12x + 3x2 Solving 2 = 11 + 12x + 3x2 Solving for variable 'x'. Combine like terms: 2 + -11 = -9 -9 + -12x + -3x2 = 11 + 12x + 3x2 + -11 + -12x + -3x2 Reorder the terms: -9 + -12x + -3x2 = 11 + -11 + 12x + -12x + 3x2 + -3x2 Combine like terms: 11 + -11 = 0 -9 + -12x + -3x2 = 0 + 12x + -12x + 3x2 + -3x2 -9 + -12x + -3x2 = 12x + -12x + 3x2 + -3x2 Combine like terms: 12x + -12x = 0 -9 + -12x + -3x2 = 0 + 3x2 + -3x2 -9 + -12x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -9 + -12x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(3 + 4x + x2) = 0 Factor a trinomial. -3((3 + x)(1 + x)) = 0 Ignore the factor -3.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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