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Simplifying b2 + 13b + 13 = 0 Reorder the terms: 13 + 13b + b2 = 0 Solving 13 + 13b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 13b + -13 + b2 = 0 + -13 Reorder the terms: 13 + -13 + 13b + b2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 13b + b2 = 0 + -13 13b + b2 = 0 + -13 Combine like terms: 0 + -13 = -13 13b + b2 = -13 The b term is 13b. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13b + 42.25 + b2 = -13 + 42.25 Reorder the terms: 42.25 + 13b + b2 = -13 + 42.25 Combine like terms: -13 + 42.25 = 29.25 42.25 + 13b + b2 = 29.25 Factor a perfect square on the left side: (b + 6.5)(b + 6.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (b + 6.5) equal to 5.408326913 and -5.408326913.Subproblem 1
b + 6.5 = 5.408326913 Simplifying b + 6.5 = 5.408326913 Reorder the terms: 6.5 + b = 5.408326913 Solving 6.5 + b = 5.408326913 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + b = 5.408326913 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + b = 5.408326913 + -6.5 b = 5.408326913 + -6.5 Combine like terms: 5.408326913 + -6.5 = -1.091673087 b = -1.091673087 Simplifying b = -1.091673087Subproblem 2
b + 6.5 = -5.408326913 Simplifying b + 6.5 = -5.408326913 Reorder the terms: 6.5 + b = -5.408326913 Solving 6.5 + b = -5.408326913 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + b = -5.408326913 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + b = -5.408326913 + -6.5 b = -5.408326913 + -6.5 Combine like terms: -5.408326913 + -6.5 = -11.908326913 b = -11.908326913 Simplifying b = -11.908326913Solution
The solution to the problem is based on the solutions from the subproblems. b = {-1.091673087, -11.908326913}
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