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Simplifying 7b2 + -31b = 20 + -8b Reorder the terms: -31b + 7b2 = 20 + -8b Solving -31b + 7b2 = 20 + -8b Solving for variable 'b'. Reorder the terms: -20 + -31b + 8b + 7b2 = 20 + -8b + -20 + 8b Combine like terms: -31b + 8b = -23b -20 + -23b + 7b2 = 20 + -8b + -20 + 8b Reorder the terms: -20 + -23b + 7b2 = 20 + -20 + -8b + 8b Combine like terms: 20 + -20 = 0 -20 + -23b + 7b2 = 0 + -8b + 8b -20 + -23b + 7b2 = -8b + 8b Combine like terms: -8b + 8b = 0 -20 + -23b + 7b2 = 0 Factor a trinomial. (-5 + -7b)(4 + -1b) = 0Subproblem 1
Set the factor '(-5 + -7b)' equal to zero and attempt to solve: Simplifying -5 + -7b = 0 Solving -5 + -7b = 0 Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -7b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7b = 0 + 5 -7b = 0 + 5 Combine like terms: 0 + 5 = 5 -7b = 5 Divide each side by '-7'. b = -0.7142857143 Simplifying b = -0.7142857143Subproblem 2
Set the factor '(4 + -1b)' equal to zero and attempt to solve: Simplifying 4 + -1b = 0 Solving 4 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1b = 0 + -4 -1b = 0 + -4 Combine like terms: 0 + -4 = -4 -1b = -4 Divide each side by '-1'. b = 4 Simplifying b = 4Solution
b = {-0.7142857143, 4}
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