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Simplifying 5b2 + 31b = 28 Reorder the terms: 31b + 5b2 = 28 Solving 31b + 5b2 = 28 Solving for variable 'b'. Reorder the terms: -28 + 31b + 5b2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 31b + 5b2 = 0 Factor a trinomial. (-7 + -1b)(4 + -5b) = 0Subproblem 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 '(4 + -5b)' equal to zero and attempt to solve: Simplifying 4 + -5b = 0 Solving 4 + -5b = 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 + -5b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5b = 0 + -4 -5b = 0 + -4 Combine like terms: 0 + -4 = -4 -5b = -4 Divide each side by '-5'. b = 0.8 Simplifying b = 0.8Solution
b = {-7, 0.8}
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