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Simplifying b2 + -8b + 16 = 7 Reorder the terms: 16 + -8b + b2 = 7 Solving 16 + -8b + b2 = 7 Solving for variable 'b'. Reorder the terms: 16 + -7 + -8b + b2 = 7 + -7 Combine like terms: 16 + -7 = 9 9 + -8b + b2 = 7 + -7 Combine like terms: 7 + -7 = 0 9 + -8b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -8b + -9 + b2 = 0 + -9 Reorder the terms: 9 + -9 + -8b + b2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8b + b2 = 0 + -9 -8b + b2 = 0 + -9 Combine like terms: 0 + -9 = -9 -8b + b2 = -9 The b term is -8b. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8b + 16 + b2 = -9 + 16 Reorder the terms: 16 + -8b + b2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + -8b + b2 = 7 Factor a perfect square on the left side: (b + -4)(b + -4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (b + -4) equal to 2.645751311 and -2.645751311.Subproblem 1
b + -4 = 2.645751311 Simplifying b + -4 = 2.645751311 Reorder the terms: -4 + b = 2.645751311 Solving -4 + b = 2.645751311 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + b = 2.645751311 + 4 b = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 b = 6.645751311 Simplifying b = 6.645751311Subproblem 2
b + -4 = -2.645751311 Simplifying b + -4 = -2.645751311 Reorder the terms: -4 + b = -2.645751311 Solving -4 + b = -2.645751311 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + b = -2.645751311 + 4 b = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 b = 1.354248689 Simplifying b = 1.354248689Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.645751311, 1.354248689}
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