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Simplifying 12x2 + 7x + 2 = x + 8 Reorder the terms: 2 + 7x + 12x2 = x + 8 Reorder the terms: 2 + 7x + 12x2 = 8 + x Solving 2 + 7x + 12x2 = 8 + x Solving for variable 'x'. Reorder the terms: 2 + -8 + 7x + -1x + 12x2 = 8 + x + -8 + -1x Combine like terms: 2 + -8 = -6 -6 + 7x + -1x + 12x2 = 8 + x + -8 + -1x Combine like terms: 7x + -1x = 6x -6 + 6x + 12x2 = 8 + x + -8 + -1x Reorder the terms: -6 + 6x + 12x2 = 8 + -8 + x + -1x Combine like terms: 8 + -8 = 0 -6 + 6x + 12x2 = 0 + x + -1x -6 + 6x + 12x2 = x + -1x Combine like terms: x + -1x = 0 -6 + 6x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-1 + x + 2x2) = 0 Factor a trinomial. 6((-1 + -1x)(1 + -2x)) = 0 Ignore the factor 6.Subproblem 1
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 = -1Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-1, 0.5}
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