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Simplifying 12 = 3x2 + -9x + 18 Reorder the terms: 12 = 18 + -9x + 3x2 Solving 12 = 18 + -9x + 3x2 Solving for variable 'x'. Combine like terms: 12 + -18 = -6 -6 + 9x + -3x2 = 18 + -9x + 3x2 + -18 + 9x + -3x2 Reorder the terms: -6 + 9x + -3x2 = 18 + -18 + -9x + 9x + 3x2 + -3x2 Combine like terms: 18 + -18 = 0 -6 + 9x + -3x2 = 0 + -9x + 9x + 3x2 + -3x2 -6 + 9x + -3x2 = -9x + 9x + 3x2 + -3x2 Combine like terms: -9x + 9x = 0 -6 + 9x + -3x2 = 0 + 3x2 + -3x2 -6 + 9x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -6 + 9x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 3x + -1x2) = 0 Factor a trinomial. 3((-2 + x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {2, 1}
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