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Simplifying b2 + 8b + -60 = 0 Reorder the terms: -60 + 8b + b2 = 0 Solving -60 + 8b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 8b + 60 + b2 = 0 + 60 Reorder the terms: -60 + 60 + 8b + b2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 8b + b2 = 0 + 60 8b + b2 = 0 + 60 Combine like terms: 0 + 60 = 60 8b + b2 = 60 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 = 60 + 16 Reorder the terms: 16 + 8b + b2 = 60 + 16 Combine like terms: 60 + 16 = 76 16 + 8b + b2 = 76 Factor a perfect square on the left side: (b + 4)(b + 4) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (b + 4) equal to 8.717797887 and -8.717797887.Subproblem 1
b + 4 = 8.717797887 Simplifying b + 4 = 8.717797887 Reorder the terms: 4 + b = 8.717797887 Solving 4 + b = 8.717797887 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 = 8.717797887 + -4 Combine like terms: 4 + -4 = 0 0 + b = 8.717797887 + -4 b = 8.717797887 + -4 Combine like terms: 8.717797887 + -4 = 4.717797887 b = 4.717797887 Simplifying b = 4.717797887Subproblem 2
b + 4 = -8.717797887 Simplifying b + 4 = -8.717797887 Reorder the terms: 4 + b = -8.717797887 Solving 4 + b = -8.717797887 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 = -8.717797887 + -4 Combine like terms: 4 + -4 = 0 0 + b = -8.717797887 + -4 b = -8.717797887 + -4 Combine like terms: -8.717797887 + -4 = -12.717797887 b = -12.717797887 Simplifying b = -12.717797887Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.717797887, -12.717797887}
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