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Simplifying 6x2 + -12x + -11 = 7 Reorder the terms: -11 + -12x + 6x2 = 7 Solving -11 + -12x + 6x2 = 7 Solving for variable 'x'. Reorder the terms: -11 + -7 + -12x + 6x2 = 7 + -7 Combine like terms: -11 + -7 = -18 -18 + -12x + 6x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -18 + -12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + -2x + x2) = 0 Factor a trinomial. 6((-1 + -1x)(3 + -1x)) = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-1, 3}
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