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Simplifying 9b2 + 18b + -31 = 9 Reorder the terms: -31 + 18b + 9b2 = 9 Solving -31 + 18b + 9b2 = 9 Solving for variable 'b'. Reorder the terms: -31 + -9 + 18b + 9b2 = 9 + -9 Combine like terms: -31 + -9 = -40 -40 + 18b + 9b2 = 9 + -9 Combine like terms: 9 + -9 = 0 -40 + 18b + 9b2 = 0 Factor a trinomial. (-10 + -3b)(4 + -3b) = 0Subproblem 1
Set the factor '(-10 + -3b)' equal to zero and attempt to solve: Simplifying -10 + -3b = 0 Solving -10 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -3b = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -3b = 0 + 10 -3b = 0 + 10 Combine like terms: 0 + 10 = 10 -3b = 10 Divide each side by '-3'. b = -3.333333333 Simplifying b = -3.333333333Subproblem 2
Set the factor '(4 + -3b)' equal to zero and attempt to solve: Simplifying 4 + -3b = 0 Solving 4 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3b = 0 + -4 -3b = 0 + -4 Combine like terms: 0 + -4 = -4 -3b = -4 Divide each side by '-3'. b = 1.333333333 Simplifying b = 1.333333333Solution
b = {-3.333333333, 1.333333333}
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