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Simplifying 0 = b2 + -5b + -84 Reorder the terms: 0 = -84 + -5b + b2 Solving 0 = -84 + -5b + b2 Solving for variable 'b'. Combine like terms: 0 + 84 = 84 84 + 5b + -1b2 = -84 + -5b + b2 + 84 + 5b + -1b2 Reorder the terms: 84 + 5b + -1b2 = -84 + 84 + -5b + 5b + b2 + -1b2 Combine like terms: -84 + 84 = 0 84 + 5b + -1b2 = 0 + -5b + 5b + b2 + -1b2 84 + 5b + -1b2 = -5b + 5b + b2 + -1b2 Combine like terms: -5b + 5b = 0 84 + 5b + -1b2 = 0 + b2 + -1b2 84 + 5b + -1b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 84 + 5b + -1b2 = 0 Factor a trinomial. (12 + -1b)(7 + b) = 0Subproblem 1
Set the factor '(12 + -1b)' equal to zero and attempt to solve: Simplifying 12 + -1b = 0 Solving 12 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1b = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1b = 0 + -12 -1b = 0 + -12 Combine like terms: 0 + -12 = -12 -1b = -12 Divide each side by '-1'. b = 12 Simplifying b = 12Subproblem 2
Set the factor '(7 + b)' equal to zero and attempt to solve: Simplifying 7 + b = 0 Solving 7 + b = 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 + b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + b = 0 + -7 b = 0 + -7 Combine like terms: 0 + -7 = -7 b = -7 Simplifying b = -7Solution
b = {12, -7}
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