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Simplifying 3b2 + 20b + 31 = 6 Reorder the terms: 31 + 20b + 3b2 = 6 Solving 31 + 20b + 3b2 = 6 Solving for variable 'b'. Reorder the terms: 31 + -6 + 20b + 3b2 = 6 + -6 Combine like terms: 31 + -6 = 25 25 + 20b + 3b2 = 6 + -6 Combine like terms: 6 + -6 = 0 25 + 20b + 3b2 = 0 Factor a trinomial. (5 + b)(5 + 3b) = 0Subproblem 1
Set the factor '(5 + b)' equal to zero and attempt to solve: Simplifying 5 + b = 0 Solving 5 + b = 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 + b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + b = 0 + -5 b = 0 + -5 Combine like terms: 0 + -5 = -5 b = -5 Simplifying b = -5Subproblem 2
Set the factor '(5 + 3b)' equal to zero and attempt to solve: Simplifying 5 + 3b = 0 Solving 5 + 3b = 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 + 3b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3b = 0 + -5 3b = 0 + -5 Combine like terms: 0 + -5 = -5 3b = -5 Divide each side by '3'. b = -1.666666667 Simplifying b = -1.666666667Solution
b = {-5, -1.666666667}
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