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Simplifying 0 = 12x2 + -36x + 27 Reorder the terms: 0 = 27 + -36x + 12x2 Solving 0 = 27 + -36x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -27 = -27 -27 + 36x + -12x2 = 27 + -36x + 12x2 + -27 + 36x + -12x2 Reorder the terms: -27 + 36x + -12x2 = 27 + -27 + -36x + 36x + 12x2 + -12x2 Combine like terms: 27 + -27 = 0 -27 + 36x + -12x2 = 0 + -36x + 36x + 12x2 + -12x2 -27 + 36x + -12x2 = -36x + 36x + 12x2 + -12x2 Combine like terms: -36x + 36x = 0 -27 + 36x + -12x2 = 0 + 12x2 + -12x2 -27 + 36x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -27 + 36x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 12x + -4x2) = 0 Factor a trinomial. 3((-3 + 2x)(3 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {1.5, 1.5}
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