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Simplifying 12 = 2x2 + -6x + 4 Reorder the terms: 12 = 4 + -6x + 2x2 Solving 12 = 4 + -6x + 2x2 Solving for variable 'x'. Combine like terms: 12 + -4 = 8 8 + 6x + -2x2 = 4 + -6x + 2x2 + -4 + 6x + -2x2 Reorder the terms: 8 + 6x + -2x2 = 4 + -4 + -6x + 6x + 2x2 + -2x2 Combine like terms: 4 + -4 = 0 8 + 6x + -2x2 = 0 + -6x + 6x + 2x2 + -2x2 8 + 6x + -2x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 8 + 6x + -2x2 = 0 + 2x2 + -2x2 8 + 6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 8 + 6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 3x + -1x2) = 0 Factor a trinomial. 2((4 + -1x)(1 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {4, -1}
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