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Simplifying b2 = 4b + 21 Reorder the terms: b2 = 21 + 4b Solving b2 = 21 + 4b Solving for variable 'b'. Reorder the terms: -21 + -4b + b2 = 21 + 4b + -21 + -4b Reorder the terms: -21 + -4b + b2 = 21 + -21 + 4b + -4b Combine like terms: 21 + -21 = 0 -21 + -4b + b2 = 0 + 4b + -4b -21 + -4b + b2 = 4b + -4b Combine like terms: 4b + -4b = 0 -21 + -4b + b2 = 0 Factor a trinomial. (-3 + -1b)(7 + -1b) = 0Subproblem 1
Set the factor '(-3 + -1b)' equal to zero and attempt to solve: Simplifying -3 + -1b = 0 Solving -3 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1b = 0 + 3 -1b = 0 + 3 Combine like terms: 0 + 3 = 3 -1b = 3 Divide each side by '-1'. b = -3 Simplifying b = -3Subproblem 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 = {-3, 7}
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