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Simplifying 22x = 12x2 + 6 Reorder the terms: 22x = 6 + 12x2 Solving 22x = 6 + 12x2 Solving for variable 'x'. Reorder the terms: -6 + 22x + -12x2 = 6 + 12x2 + -6 + -12x2 Reorder the terms: -6 + 22x + -12x2 = 6 + -6 + 12x2 + -12x2 Combine like terms: 6 + -6 = 0 -6 + 22x + -12x2 = 0 + 12x2 + -12x2 -6 + 22x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -6 + 22x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 11x + -6x2) = 0 Factor a trinomial. 2((-3 + 2x)(1 + -3x)) = 0 Ignore the factor 2.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 '(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 = {1.5, 0.3333333333}
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