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Simplifying 216 = (2x + 14)(x + 4) Reorder the terms: 216 = (14 + 2x)(x + 4) Reorder the terms: 216 = (14 + 2x)(4 + x) Multiply (14 + 2x) * (4 + x) 216 = (14(4 + x) + 2x * (4 + x)) 216 = ((4 * 14 + x * 14) + 2x * (4 + x)) 216 = ((56 + 14x) + 2x * (4 + x)) 216 = (56 + 14x + (4 * 2x + x * 2x)) 216 = (56 + 14x + (8x + 2x2)) Combine like terms: 14x + 8x = 22x 216 = (56 + 22x + 2x2) Solving 216 = 56 + 22x + 2x2 Solving for variable 'x'. Combine like terms: 216 + -56 = 160 160 + -22x + -2x2 = 56 + 22x + 2x2 + -56 + -22x + -2x2 Reorder the terms: 160 + -22x + -2x2 = 56 + -56 + 22x + -22x + 2x2 + -2x2 Combine like terms: 56 + -56 = 0 160 + -22x + -2x2 = 0 + 22x + -22x + 2x2 + -2x2 160 + -22x + -2x2 = 22x + -22x + 2x2 + -2x2 Combine like terms: 22x + -22x = 0 160 + -22x + -2x2 = 0 + 2x2 + -2x2 160 + -22x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 160 + -22x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(80 + -11x + -1x2) = 0 Factor a trinomial. 2((5 + -1x)(16 + 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 '(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 = {5, -16}
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