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Simplifying b2 + -8b + 23 = 7 Reorder the terms: 23 + -8b + b2 = 7 Solving 23 + -8b + b2 = 7 Solving for variable 'b'. Reorder the terms: 23 + -7 + -8b + b2 = 7 + -7 Combine like terms: 23 + -7 = 16 16 + -8b + b2 = 7 + -7 Combine like terms: 7 + -7 = 0 16 + -8b + b2 = 0 Factor a trinomial. (4 + -1b)(4 + -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 '(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 = 4Solution
b = {4, 4}
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