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Simplifying (b + 4)(b + 4) = 100 Reorder the terms: (4 + b)(b + 4) = 100 Reorder the terms: (4 + b)(4 + b) = 100 Multiply (4 + b) * (4 + b) (4(4 + b) + b(4 + b)) = 100 ((4 * 4 + b * 4) + b(4 + b)) = 100 ((16 + 4b) + b(4 + b)) = 100 (16 + 4b + (4 * b + b * b)) = 100 (16 + 4b + (4b + b^{2})) = 100 Combine like terms: 4b + 4b = 8b (16 + 8b + b^{2}) = 100 Solving 16 + 8b + b^{2}= 100 Solving for variable 'b'. Reorder the terms: 16 + -100 + 8b + b^{2}= 100 + -100 Combine like terms: 16 + -100 = -84 -84 + 8b + b^{2}= 100 + -100 Combine like terms: 100 + -100 = 0 -84 + 8b + b^{2}= 0 Factor a trinomial. (-14 + -1b)(6 + -1b) = 0## Subproblem 1

Set the factor '(-14 + -1b)' equal to zero and attempt to solve: Simplifying -14 + -1b = 0 Solving -14 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1b = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1b = 0 + 14 -1b = 0 + 14 Combine like terms: 0 + 14 = 14 -1b = 14 Divide each side by '-1'. b = -14 Simplifying b = -14## Subproblem 2

Set the factor '(6 + -1b)' equal to zero and attempt to solve: Simplifying 6 + -1b = 0 Solving 6 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1b = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1b = 0 + -6 -1b = 0 + -6 Combine like terms: 0 + -6 = -6 -1b = -6 Divide each side by '-1'. b = 6 Simplifying b = 6## Solution

b = {-14, 6}

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