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Simplifying b2 = 45 + -4b Solving b2 = 45 + -4b Solving for variable 'b'. Reorder the terms: -45 + 4b + b2 = 45 + -4b + -45 + 4b Reorder the terms: -45 + 4b + b2 = 45 + -45 + -4b + 4b Combine like terms: 45 + -45 = 0 -45 + 4b + b2 = 0 + -4b + 4b -45 + 4b + b2 = -4b + 4b Combine like terms: -4b + 4b = 0 -45 + 4b + b2 = 0 Factor a trinomial. (-9 + -1b)(5 + -1b) = 0Subproblem 1
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 = -9Subproblem 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 = {-9, 5}
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