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Simplifying 2b2 + -9b = 3b2 + -4b + -14 Reorder the terms: -9b + 2b2 = 3b2 + -4b + -14 Reorder the terms: -9b + 2b2 = -14 + -4b + 3b2 Solving -9b + 2b2 = -14 + -4b + 3b2 Solving for variable 'b'. Reorder the terms: 14 + -9b + 4b + 2b2 + -3b2 = -14 + -4b + 3b2 + 14 + 4b + -3b2 Combine like terms: -9b + 4b = -5b 14 + -5b + 2b2 + -3b2 = -14 + -4b + 3b2 + 14 + 4b + -3b2 Combine like terms: 2b2 + -3b2 = -1b2 14 + -5b + -1b2 = -14 + -4b + 3b2 + 14 + 4b + -3b2 Reorder the terms: 14 + -5b + -1b2 = -14 + 14 + -4b + 4b + 3b2 + -3b2 Combine like terms: -14 + 14 = 0 14 + -5b + -1b2 = 0 + -4b + 4b + 3b2 + -3b2 14 + -5b + -1b2 = -4b + 4b + 3b2 + -3b2 Combine like terms: -4b + 4b = 0 14 + -5b + -1b2 = 0 + 3b2 + -3b2 14 + -5b + -1b2 = 3b2 + -3b2 Combine like terms: 3b2 + -3b2 = 0 14 + -5b + -1b2 = 0 Factor a trinomial. (2 + -1b)(7 + b) = 0Subproblem 1
Set the factor '(2 + -1b)' equal to zero and attempt to solve: Simplifying 2 + -1b = 0 Solving 2 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1b = 0 + -2 -1b = 0 + -2 Combine like terms: 0 + -2 = -2 -1b = -2 Divide each side by '-1'. b = 2 Simplifying b = 2Subproblem 2
Set the factor '(7 + b)' equal to zero and attempt to solve: Simplifying 7 + b = 0 Solving 7 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + b = 0 + -7 b = 0 + -7 Combine like terms: 0 + -7 = -7 b = -7 Simplifying b = -7Solution
b = {2, -7}
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