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Simplifying b2 = 40 + -1b Solving b2 = 40 + -1b Solving for variable 'b'. Reorder the terms: -40 + b + b2 = 40 + -1b + -40 + b Reorder the terms: -40 + b + b2 = 40 + -40 + -1b + b Combine like terms: 40 + -40 = 0 -40 + b + b2 = 0 + -1b + b -40 + b + b2 = -1b + b Combine like terms: -1b + b = 0 -40 + b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + b + 40 + b2 = 0 + 40 Reorder the terms: -40 + 40 + b + b2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + b + b2 = 0 + 40 b + b2 = 0 + 40 Combine like terms: 0 + 40 = 40 b + b2 = 40 The b term is b. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. b + 0.25 + b2 = 40 + 0.25 Reorder the terms: 0.25 + b + b2 = 40 + 0.25 Combine like terms: 40 + 0.25 = 40.25 0.25 + b + b2 = 40.25 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (b + 0.5) equal to 6.34428877 and -6.34428877.Subproblem 1
b + 0.5 = 6.34428877 Simplifying b + 0.5 = 6.34428877 Reorder the terms: 0.5 + b = 6.34428877 Solving 0.5 + b = 6.34428877 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = 6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 6.34428877 + -0.5 b = 6.34428877 + -0.5 Combine like terms: 6.34428877 + -0.5 = 5.84428877 b = 5.84428877 Simplifying b = 5.84428877Subproblem 2
b + 0.5 = -6.34428877 Simplifying b + 0.5 = -6.34428877 Reorder the terms: 0.5 + b = -6.34428877 Solving 0.5 + b = -6.34428877 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = -6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -6.34428877 + -0.5 b = -6.34428877 + -0.5 Combine like terms: -6.34428877 + -0.5 = -6.84428877 b = -6.84428877 Simplifying b = -6.84428877Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.84428877, -6.84428877}
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