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Simplifying 2b2 + 17b = 14 + 5b Reorder the terms: 17b + 2b2 = 14 + 5b Solving 17b + 2b2 = 14 + 5b Solving for variable 'b'. Reorder the terms: -14 + 17b + -5b + 2b2 = 14 + 5b + -14 + -5b Combine like terms: 17b + -5b = 12b -14 + 12b + 2b2 = 14 + 5b + -14 + -5b Reorder the terms: -14 + 12b + 2b2 = 14 + -14 + 5b + -5b Combine like terms: 14 + -14 = 0 -14 + 12b + 2b2 = 0 + 5b + -5b -14 + 12b + 2b2 = 5b + -5b Combine like terms: 5b + -5b = 0 -14 + 12b + 2b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 6b + b2) = 0 Factor a trinomial. 2((-7 + -1b)(1 + -1b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -1b)' equal to zero and attempt to solve: Simplifying -7 + -1b = 0 Solving -7 + -1b = 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 + -1b = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1b = 0 + 7 -1b = 0 + 7 Combine like terms: 0 + 7 = 7 -1b = 7 Divide each side by '-1'. b = -7 Simplifying b = -7Subproblem 2
Set the factor '(1 + -1b)' equal to zero and attempt to solve: Simplifying 1 + -1b = 0 Solving 1 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1b = 0 + -1 -1b = 0 + -1 Combine like terms: 0 + -1 = -1 -1b = -1 Divide each side by '-1'. b = 1 Simplifying b = 1Solution
b = {-7, 1}
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