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Simplifying 45 = b(b + -4) Reorder the terms: 45 = b(-4 + b) 45 = (-4 * b + b * b) 45 = (-4b + b2) Solving 45 = -4b + b2 Solving for variable 'b'. Reorder the terms: 45 + 4b + -1b2 = -4b + 4b + b2 + -1b2 Combine like terms: -4b + 4b = 0 45 + 4b + -1b2 = 0 + b2 + -1b2 45 + 4b + -1b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 45 + 4b + -1b2 = 0 Factor a trinomial. (9 + -1b)(5 + b) = 0Subproblem 1
Set the factor '(9 + -1b)' equal to zero and attempt to solve: Simplifying 9 + -1b = 0 Solving 9 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1b = 0 + -9 -1b = 0 + -9 Combine like terms: 0 + -9 = -9 -1b = -9 Divide each side by '-1'. b = 9 Simplifying b = 9Subproblem 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 = {9, -5}
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