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Simplifying (23 + -1b) * b = 130 Reorder the terms for easier multiplication: b(23 + -1b) = 130 (23 * b + -1b * b) = 130 (23b + -1b2) = 130 Solving 23b + -1b2 = 130 Solving for variable 'b'. Reorder the terms: -130 + 23b + -1b2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + 23b + -1b2 = 0 Factor a trinomial. (-13 + b)(10 + -1b) = 0Subproblem 1
Set the factor '(-13 + b)' equal to zero and attempt to solve: Simplifying -13 + b = 0 Solving -13 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + b = 0 + 13 Combine like terms: -13 + 13 = 0 0 + b = 0 + 13 b = 0 + 13 Combine like terms: 0 + 13 = 13 b = 13 Simplifying b = 13Subproblem 2
Set the factor '(10 + -1b)' equal to zero and attempt to solve: Simplifying 10 + -1b = 0 Solving 10 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1b = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1b = 0 + -10 -1b = 0 + -10 Combine like terms: 0 + -10 = -10 -1b = -10 Divide each side by '-1'. b = 10 Simplifying b = 10Solution
b = {13, 10}
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