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Simplifying 6b2 + 25b + 9 = -16 Reorder the terms: 9 + 25b + 6b2 = -16 Solving 9 + 25b + 6b2 = -16 Solving for variable 'b'. Reorder the terms: 9 + 16 + 25b + 6b2 = -16 + 16 Combine like terms: 9 + 16 = 25 25 + 25b + 6b2 = -16 + 16 Combine like terms: -16 + 16 = 0 25 + 25b + 6b2 = 0 Factor a trinomial. (5 + 2b)(5 + 3b) = 0Subproblem 1
Set the factor '(5 + 2b)' equal to zero and attempt to solve: Simplifying 5 + 2b = 0 Solving 5 + 2b = 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 + 2b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2b = 0 + -5 2b = 0 + -5 Combine like terms: 0 + -5 = -5 2b = -5 Divide each side by '2'. b = -2.5 Simplifying b = -2.5Subproblem 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 = {-2.5, -1.666666667}
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