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Simplifying b2 + -12b = 2b + -45 Reorder the terms: -12b + b2 = 2b + -45 Reorder the terms: -12b + b2 = -45 + 2b Solving -12b + b2 = -45 + 2b Solving for variable 'b'. Reorder the terms: 45 + -12b + -2b + b2 = -45 + 2b + 45 + -2b Combine like terms: -12b + -2b = -14b 45 + -14b + b2 = -45 + 2b + 45 + -2b Reorder the terms: 45 + -14b + b2 = -45 + 45 + 2b + -2b Combine like terms: -45 + 45 = 0 45 + -14b + b2 = 0 + 2b + -2b 45 + -14b + b2 = 2b + -2b Combine like terms: 2b + -2b = 0 45 + -14b + b2 = 0 Factor a trinomial. (5 + -1b)(9 + -1b) = 0Subproblem 1
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 = 5Subproblem 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 = {5, 9}
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