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Simplifying (x + 2)(x + 4) = 120 Reorder the terms: (2 + x)(x + 4) = 120 Reorder the terms: (2 + x)(4 + x) = 120 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = 120 ((4 * 2 + x * 2) + x(4 + x)) = 120 ((8 + 2x) + x(4 + x)) = 120 (8 + 2x + (4 * x + x * x)) = 120 (8 + 2x + (4x + x2)) = 120 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = 120 Solving 8 + 6x + x2 = 120 Solving for variable 'x'. Reorder the terms: 8 + -120 + 6x + x2 = 120 + -120 Combine like terms: 8 + -120 = -112 -112 + 6x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -112 + 6x + x2 = 0 Factor a trinomial. (-14 + -1x)(8 + -1x) = 0Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve: Simplifying -14 + -1x = 0 Solving -14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1x = 0 + 14 -1x = 0 + 14 Combine like terms: 0 + 14 = 14 -1x = 14 Divide each side by '-1'. x = -14 Simplifying x = -14Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-14, 8}
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