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Simplifying b(b + 26) = 9(8 + 3b) Reorder the terms: b(26 + b) = 9(8 + 3b) (26 * b + b * b) = 9(8 + 3b) (26b + b2) = 9(8 + 3b) 26b + b2 = (8 * 9 + 3b * 9) 26b + b2 = (72 + 27b) Solving 26b + b2 = 72 + 27b Solving for variable 'b'. Reorder the terms: -72 + 26b + -27b + b2 = 72 + 27b + -72 + -27b Combine like terms: 26b + -27b = -1b -72 + -1b + b2 = 72 + 27b + -72 + -27b Reorder the terms: -72 + -1b + b2 = 72 + -72 + 27b + -27b Combine like terms: 72 + -72 = 0 -72 + -1b + b2 = 0 + 27b + -27b -72 + -1b + b2 = 27b + -27b Combine like terms: 27b + -27b = 0 -72 + -1b + b2 = 0 Factor a trinomial. (-8 + -1b)(9 + -1b) = 0Subproblem 1
Set the factor '(-8 + -1b)' equal to zero and attempt to solve: Simplifying -8 + -1b = 0 Solving -8 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1b = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1b = 0 + 8 -1b = 0 + 8 Combine like terms: 0 + 8 = 8 -1b = 8 Divide each side by '-1'. b = -8 Simplifying b = -8Subproblem 2
Set the factor '(9 + -1b)' equal to zero and attempt to solve: Simplifying 9 + -1b = 0 Solving 9 + -1b = 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 + -1b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1b = 0 + -9 -1b = 0 + -9 Combine like terms: 0 + -9 = -9 -1b = -9 Divide each side by '-1'. b = 9 Simplifying b = 9Solution
b = {-8, 9}
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