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Simplifying 112 = (x + 4)(2x + 6) Reorder the terms: 112 = (4 + x)(2x + 6) Reorder the terms: 112 = (4 + x)(6 + 2x) Multiply (4 + x) * (6 + 2x) 112 = (4(6 + 2x) + x(6 + 2x)) 112 = ((6 * 4 + 2x * 4) + x(6 + 2x)) 112 = ((24 + 8x) + x(6 + 2x)) 112 = (24 + 8x + (6 * x + 2x * x)) 112 = (24 + 8x + (6x + 2x2)) Combine like terms: 8x + 6x = 14x 112 = (24 + 14x + 2x2) Solving 112 = 24 + 14x + 2x2 Solving for variable 'x'. Combine like terms: 112 + -24 = 88 88 + -14x + -2x2 = 24 + 14x + 2x2 + -24 + -14x + -2x2 Reorder the terms: 88 + -14x + -2x2 = 24 + -24 + 14x + -14x + 2x2 + -2x2 Combine like terms: 24 + -24 = 0 88 + -14x + -2x2 = 0 + 14x + -14x + 2x2 + -2x2 88 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2 Combine like terms: 14x + -14x = 0 88 + -14x + -2x2 = 0 + 2x2 + -2x2 88 + -14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 88 + -14x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(44 + -7x + -1x2) = 0 Factor a trinomial. 2((4 + -1x)(11 + 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 '(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 = {4, -11}
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