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Simplifying b2 = 5b + 14 Reorder the terms: b2 = 14 + 5b Solving b2 = 14 + 5b Solving for variable 'b'. Reorder the terms: -14 + -5b + b2 = 14 + 5b + -14 + -5b Reorder the terms: -14 + -5b + b2 = 14 + -14 + 5b + -5b Combine like terms: 14 + -14 = 0 -14 + -5b + b2 = 0 + 5b + -5b -14 + -5b + b2 = 5b + -5b Combine like terms: 5b + -5b = 0 -14 + -5b + b2 = 0 Factor a trinomial. (-2 + -1b)(7 + -1b) = 0Subproblem 1
Set the factor '(-2 + -1b)' equal to zero and attempt to solve: Simplifying -2 + -1b = 0 Solving -2 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1b = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1b = 0 + 2 -1b = 0 + 2 Combine like terms: 0 + 2 = 2 -1b = 2 Divide each side by '-1'. b = -2 Simplifying b = -2Subproblem 2
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 = 7Solution
b = {-2, 7}
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