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Simplifying 2b2 = 19b + -24 Reorder the terms: 2b2 = -24 + 19b Solving 2b2 = -24 + 19b Solving for variable 'b'. Reorder the terms: 24 + -19b + 2b2 = -24 + 19b + 24 + -19b Reorder the terms: 24 + -19b + 2b2 = -24 + 24 + 19b + -19b Combine like terms: -24 + 24 = 0 24 + -19b + 2b2 = 0 + 19b + -19b 24 + -19b + 2b2 = 19b + -19b Combine like terms: 19b + -19b = 0 24 + -19b + 2b2 = 0 Factor a trinomial. (3 + -2b)(8 + -1b) = 0Subproblem 1
Set the factor '(3 + -2b)' equal to zero and attempt to solve: Simplifying 3 + -2b = 0 Solving 3 + -2b = 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 + -2b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2b = 0 + -3 -2b = 0 + -3 Combine like terms: 0 + -3 = -3 -2b = -3 Divide each side by '-2'. b = 1.5 Simplifying b = 1.5Subproblem 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 = {1.5, 8}
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