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Simplifying 38x = 6x2 + 12 Reorder the terms: 38x = 12 + 6x2 Solving 38x = 12 + 6x2 Solving for variable 'x'. Reorder the terms: -12 + 38x + -6x2 = 12 + 6x2 + -12 + -6x2 Reorder the terms: -12 + 38x + -6x2 = 12 + -12 + 6x2 + -6x2 Combine like terms: 12 + -12 = 0 -12 + 38x + -6x2 = 0 + 6x2 + -6x2 -12 + 38x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -12 + 38x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 19x + -3x2) = 0 Factor a trinomial. 2((-6 + x)(1 + -3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 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 = {6, 0.3333333333}
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