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Simplifying 9b2 + -44b = -3b + -5 + b2 Reorder the terms: -44b + 9b2 = -3b + -5 + b2 Reorder the terms: -44b + 9b2 = -5 + -3b + b2 Solving -44b + 9b2 = -5 + -3b + b2 Solving for variable 'b'. Reorder the terms: 5 + -44b + 3b + 9b2 + -1b2 = -5 + -3b + b2 + 5 + 3b + -1b2 Combine like terms: -44b + 3b = -41b 5 + -41b + 9b2 + -1b2 = -5 + -3b + b2 + 5 + 3b + -1b2 Combine like terms: 9b2 + -1b2 = 8b2 5 + -41b + 8b2 = -5 + -3b + b2 + 5 + 3b + -1b2 Reorder the terms: 5 + -41b + 8b2 = -5 + 5 + -3b + 3b + b2 + -1b2 Combine like terms: -5 + 5 = 0 5 + -41b + 8b2 = 0 + -3b + 3b + b2 + -1b2 5 + -41b + 8b2 = -3b + 3b + b2 + -1b2 Combine like terms: -3b + 3b = 0 5 + -41b + 8b2 = 0 + b2 + -1b2 5 + -41b + 8b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 5 + -41b + 8b2 = 0 Factor a trinomial. (1 + -8b)(5 + -1b) = 0Subproblem 1
Set the factor '(1 + -8b)' equal to zero and attempt to solve: Simplifying 1 + -8b = 0 Solving 1 + -8b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -8b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8b = 0 + -1 -8b = 0 + -1 Combine like terms: 0 + -1 = -1 -8b = -1 Divide each side by '-8'. b = 0.125 Simplifying b = 0.125Subproblem 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 = {0.125, 5}
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