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Simplifying (b + 8)(b + 4) = 5 Reorder the terms: (8 + b)(b + 4) = 5 Reorder the terms: (8 + b)(4 + b) = 5 Multiply (8 + b) * (4 + b) (8(4 + b) + b(4 + b)) = 5 ((4 * 8 + b * 8) + b(4 + b)) = 5 ((32 + 8b) + b(4 + b)) = 5 (32 + 8b + (4 * b + b * b)) = 5 (32 + 8b + (4b + b2)) = 5 Combine like terms: 8b + 4b = 12b (32 + 12b + b2) = 5 Solving 32 + 12b + b2 = 5 Solving for variable 'b'. Reorder the terms: 32 + -5 + 12b + b2 = 5 + -5 Combine like terms: 32 + -5 = 27 27 + 12b + b2 = 5 + -5 Combine like terms: 5 + -5 = 0 27 + 12b + b2 = 0 Factor a trinomial. (9 + b)(3 + b) = 0Subproblem 1
Set the factor '(9 + b)' equal to zero and attempt to solve: Simplifying 9 + b = 0 Solving 9 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + b = 0 + -9 b = 0 + -9 Combine like terms: 0 + -9 = -9 b = -9 Simplifying b = -9Subproblem 2
Set the factor '(3 + b)' equal to zero and attempt to solve: Simplifying 3 + b = 0 Solving 3 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + b = 0 + -3 b = 0 + -3 Combine like terms: 0 + -3 = -3 b = -3 Simplifying b = -3Solution
b = {-9, -3}
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