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Simplifying b2 + -8b + 23 = 8 Reorder the terms: 23 + -8b + b2 = 8 Solving 23 + -8b + b2 = 8 Solving for variable 'b'. Reorder the terms: 23 + -8 + -8b + b2 = 8 + -8 Combine like terms: 23 + -8 = 15 15 + -8b + b2 = 8 + -8 Combine like terms: 8 + -8 = 0 15 + -8b + b2 = 0 Factor a trinomial. (3 + -1b)(5 + -1b) = 0Subproblem 1
Set the factor '(3 + -1b)' equal to zero and attempt to solve: Simplifying 3 + -1b = 0 Solving 3 + -1b = 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 + -1b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1b = 0 + -3 -1b = 0 + -3 Combine like terms: 0 + -3 = -3 -1b = -3 Divide each side by '-1'. b = 3 Simplifying b = 3Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve: Simplifying 5 + -1b = 0 Solving 5 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1b = 0 + -5 -1b = 0 + -5 Combine like terms: 0 + -5 = -5 -1b = -5 Divide each side by '-1'. b = 5 Simplifying b = 5Solution
b = {3, 5}
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