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Simplifying 234 = (x + 3)(2x + 14) Reorder the terms: 234 = (3 + x)(2x + 14) Reorder the terms: 234 = (3 + x)(14 + 2x) Multiply (3 + x) * (14 + 2x) 234 = (3(14 + 2x) + x(14 + 2x)) 234 = ((14 * 3 + 2x * 3) + x(14 + 2x)) 234 = ((42 + 6x) + x(14 + 2x)) 234 = (42 + 6x + (14 * x + 2x * x)) 234 = (42 + 6x + (14x + 2x2)) Combine like terms: 6x + 14x = 20x 234 = (42 + 20x + 2x2) Solving 234 = 42 + 20x + 2x2 Solving for variable 'x'. Combine like terms: 234 + -42 = 192 192 + -20x + -2x2 = 42 + 20x + 2x2 + -42 + -20x + -2x2 Reorder the terms: 192 + -20x + -2x2 = 42 + -42 + 20x + -20x + 2x2 + -2x2 Combine like terms: 42 + -42 = 0 192 + -20x + -2x2 = 0 + 20x + -20x + 2x2 + -2x2 192 + -20x + -2x2 = 20x + -20x + 2x2 + -2x2 Combine like terms: 20x + -20x = 0 192 + -20x + -2x2 = 0 + 2x2 + -2x2 192 + -20x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 192 + -20x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(96 + -10x + -1x2) = 0 Factor a trinomial. 2((6 + -1x)(16 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve: Simplifying 16 + x = 0 Solving 16 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + x = 0 + -16 x = 0 + -16 Combine like terms: 0 + -16 = -16 x = -16 Simplifying x = -16Solution
x = {6, -16}
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