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Simplifying 27x2 = 36x + 96 Reorder the terms: 27x2 = 96 + 36x Solving 27x2 = 96 + 36x Solving for variable 'x'. Reorder the terms: -96 + -36x + 27x2 = 96 + 36x + -96 + -36x Reorder the terms: -96 + -36x + 27x2 = 96 + -96 + 36x + -36x Combine like terms: 96 + -96 = 0 -96 + -36x + 27x2 = 0 + 36x + -36x -96 + -36x + 27x2 = 36x + -36x Combine like terms: 36x + -36x = 0 -96 + -36x + 27x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-32 + -12x + 9x2) = 0 Factor a trinomial. 3((-4 + -3x)(8 + -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 '(8 + -3x)' equal to zero and attempt to solve: Simplifying 8 + -3x = 0 Solving 8 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3x = 0 + -8 -3x = 0 + -8 Combine like terms: 0 + -8 = -8 -3x = -8 Divide each side by '-3'. x = 2.666666667 Simplifying x = 2.666666667Solution
x = {-1.333333333, 2.666666667}
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