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Simplifying 4 = 2x2 + 12x + -106 Reorder the terms: 4 = -106 + 12x + 2x2 Solving 4 = -106 + 12x + 2x2 Solving for variable 'x'. Combine like terms: 4 + 106 = 110 110 + -12x + -2x2 = -106 + 12x + 2x2 + 106 + -12x + -2x2 Reorder the terms: 110 + -12x + -2x2 = -106 + 106 + 12x + -12x + 2x2 + -2x2 Combine like terms: -106 + 106 = 0 110 + -12x + -2x2 = 0 + 12x + -12x + 2x2 + -2x2 110 + -12x + -2x2 = 12x + -12x + 2x2 + -2x2 Combine like terms: 12x + -12x = 0 110 + -12x + -2x2 = 0 + 2x2 + -2x2 110 + -12x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 110 + -12x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(55 + -6x + -1x2) = 0 Factor a trinomial. 2((5 + -1x)(11 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(11 + x)' equal to zero and attempt to solve: Simplifying 11 + x = 0 Solving 11 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + x = 0 + -11 x = 0 + -11 Combine like terms: 0 + -11 = -11 x = -11 Simplifying x = -11Solution
x = {5, -11}
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