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Simplifying b = b2 + 7b + -27 Reorder the terms: b = -27 + 7b + b2 Solving b = -27 + 7b + b2 Solving for variable 'b'. Reorder the terms: 27 + b + -7b + -1b2 = -27 + 7b + b2 + 27 + -7b + -1b2 Combine like terms: b + -7b = -6b 27 + -6b + -1b2 = -27 + 7b + b2 + 27 + -7b + -1b2 Reorder the terms: 27 + -6b + -1b2 = -27 + 27 + 7b + -7b + b2 + -1b2 Combine like terms: -27 + 27 = 0 27 + -6b + -1b2 = 0 + 7b + -7b + b2 + -1b2 27 + -6b + -1b2 = 7b + -7b + b2 + -1b2 Combine like terms: 7b + -7b = 0 27 + -6b + -1b2 = 0 + b2 + -1b2 27 + -6b + -1b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 27 + -6b + -1b2 = 0 Factor a trinomial. (3 + -1b)(9 + b) = 0Subproblem 1
Set the factor '(3 + -1b)' equal to zero and attempt to solve: Simplifying 3 + -1b = 0 Solving 3 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1b = 0 + -3 -1b = 0 + -3 Combine like terms: 0 + -3 = -3 -1b = -3 Divide each side by '-1'. b = 3 Simplifying b = 3Subproblem 2
Set the factor '(9 + b)' equal to zero and attempt to solve: Simplifying 9 + b = 0 Solving 9 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + b = 0 + -9 b = 0 + -9 Combine like terms: 0 + -9 = -9 b = -9 Simplifying b = -9Solution
b = {3, -9}
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