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Simplifying 27x2 = 12 + -27x Solving 27x2 = 12 + -27x Solving for variable 'x'. Reorder the terms: -12 + 27x + 27x2 = 12 + -27x + -12 + 27x Reorder the terms: -12 + 27x + 27x2 = 12 + -12 + -27x + 27x Combine like terms: 12 + -12 = 0 -12 + 27x + 27x2 = 0 + -27x + 27x -12 + 27x + 27x2 = -27x + 27x Combine like terms: -27x + 27x = 0 -12 + 27x + 27x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 9x + 9x2) = 0 Factor a trinomial. 3((-4 + -3x)(1 + -3x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 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 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333Subproblem 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 = {-1.333333333, 0.3333333333}
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