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Simplifying b2 + -11b = 10 Reorder the terms: -11b + b2 = 10 Solving -11b + b2 = 10 Solving for variable 'b'. Reorder the terms: -10 + -11b + b2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -11b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -11b + 10 + b2 = 0 + 10 Reorder the terms: -10 + 10 + -11b + b2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -11b + b2 = 0 + 10 -11b + b2 = 0 + 10 Combine like terms: 0 + 10 = 10 -11b + b2 = 10 The b term is -11b. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11b + 30.25 + b2 = 10 + 30.25 Reorder the terms: 30.25 + -11b + b2 = 10 + 30.25 Combine like terms: 10 + 30.25 = 40.25 30.25 + -11b + b2 = 40.25 Factor a perfect square on the left side: (b + -5.5)(b + -5.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (b + -5.5) equal to 6.34428877 and -6.34428877.Subproblem 1
b + -5.5 = 6.34428877 Simplifying b + -5.5 = 6.34428877 Reorder the terms: -5.5 + b = 6.34428877 Solving -5.5 + b = 6.34428877 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + b = 6.34428877 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + b = 6.34428877 + 5.5 b = 6.34428877 + 5.5 Combine like terms: 6.34428877 + 5.5 = 11.84428877 b = 11.84428877 Simplifying b = 11.84428877Subproblem 2
b + -5.5 = -6.34428877 Simplifying b + -5.5 = -6.34428877 Reorder the terms: -5.5 + b = -6.34428877 Solving -5.5 + b = -6.34428877 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + b = -6.34428877 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + b = -6.34428877 + 5.5 b = -6.34428877 + 5.5 Combine like terms: -6.34428877 + 5.5 = -0.84428877 b = -0.84428877 Simplifying b = -0.84428877Solution
The solution to the problem is based on the solutions from the subproblems. b = {11.84428877, -0.84428877}
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