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Simplifying (x + 2)(x + 4) = 24 Reorder the terms: (2 + x)(x + 4) = 24 Reorder the terms: (2 + x)(4 + x) = 24 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = 24 ((4 * 2 + x * 2) + x(4 + x)) = 24 ((8 + 2x) + x(4 + x)) = 24 (8 + 2x + (4 * x + x * x)) = 24 (8 + 2x + (4x + x2)) = 24 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = 24 Solving 8 + 6x + x2 = 24 Solving for variable 'x'. Reorder the terms: 8 + -24 + 6x + x2 = 24 + -24 Combine like terms: 8 + -24 = -16 -16 + 6x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -16 + 6x + x2 = 0 Factor a trinomial. (-8 + -1x)(2 + -1x) = 0Subproblem 1
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 = -8Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-8, 2}
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