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Simplifying b2 = 4b + 32 Reorder the terms: b2 = 32 + 4b Solving b2 = 32 + 4b Solving for variable 'b'. Reorder the terms: -32 + -4b + b2 = 32 + 4b + -32 + -4b Reorder the terms: -32 + -4b + b2 = 32 + -32 + 4b + -4b Combine like terms: 32 + -32 = 0 -32 + -4b + b2 = 0 + 4b + -4b -32 + -4b + b2 = 4b + -4b Combine like terms: 4b + -4b = 0 -32 + -4b + b2 = 0 Factor a trinomial. (-4 + -1b)(8 + -1b) = 0Subproblem 1
Set the factor '(-4 + -1b)' equal to zero and attempt to solve: Simplifying -4 + -1b = 0 Solving -4 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1b = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1b = 0 + 4 -1b = 0 + 4 Combine like terms: 0 + 4 = 4 -1b = 4 Divide each side by '-1'. b = -4 Simplifying b = -4Subproblem 2
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 = 8Solution
b = {-4, 8}
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