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