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Simplifying 2b2 = -112 + 30b Solving 2b2 = -112 + 30b Solving for variable 'b'. Reorder the terms: 112 + -30b + 2b2 = -112 + 30b + 112 + -30b Reorder the terms: 112 + -30b + 2b2 = -112 + 112 + 30b + -30b Combine like terms: -112 + 112 = 0 112 + -30b + 2b2 = 0 + 30b + -30b 112 + -30b + 2b2 = 30b + -30b Combine like terms: 30b + -30b = 0 112 + -30b + 2b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(56 + -15b + b2) = 0 Factor a trinomial. 2((7 + -1b)(8 + -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 '(8 + -1b)' equal to zero and attempt to solve: Simplifying 8 + -1b = 0 Solving 8 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1b = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1b = 0 + -8 -1b = 0 + -8 Combine like terms: 0 + -8 = -8 -1b = -8 Divide each side by '-1'. b = 8 Simplifying b = 8Solution
b = {7, 8}
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