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Simplifying b2 = -3b + 40 Reorder the terms: b2 = 40 + -3b Solving b2 = 40 + -3b Solving for variable 'b'. Reorder the terms: -40 + 3b + b2 = 40 + -3b + -40 + 3b Reorder the terms: -40 + 3b + b2 = 40 + -40 + -3b + 3b Combine like terms: 40 + -40 = 0 -40 + 3b + b2 = 0 + -3b + 3b -40 + 3b + b2 = -3b + 3b Combine like terms: -3b + 3b = 0 -40 + 3b + b2 = 0 Factor a trinomial. (-8 + -1b)(5 + -1b) = 0Subproblem 1
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 = -8Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve: Simplifying 5 + -1b = 0 Solving 5 + -1b = 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 + -1b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1b = 0 + -5 -1b = 0 + -5 Combine like terms: 0 + -5 = -5 -1b = -5 Divide each side by '-1'. b = 5 Simplifying b = 5Solution
b = {-8, 5}
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