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Simplifying b2 + 6b + -126 = 0 Reorder the terms: -126 + 6b + b2 = 0 Solving -126 + 6b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '126' to each side of the equation. -126 + 6b + 126 + b2 = 0 + 126 Reorder the terms: -126 + 126 + 6b + b2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 6b + b2 = 0 + 126 6b + b2 = 0 + 126 Combine like terms: 0 + 126 = 126 6b + b2 = 126 The b term is 6b. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6b + 9 + b2 = 126 + 9 Reorder the terms: 9 + 6b + b2 = 126 + 9 Combine like terms: 126 + 9 = 135 9 + 6b + b2 = 135 Factor a perfect square on the left side: (b + 3)(b + 3) = 135 Calculate the square root of the right side: 11.618950039 Break this problem into two subproblems by setting (b + 3) equal to 11.618950039 and -11.618950039.Subproblem 1
b + 3 = 11.618950039 Simplifying b + 3 = 11.618950039 Reorder the terms: 3 + b = 11.618950039 Solving 3 + b = 11.618950039 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = 11.618950039 + -3 Combine like terms: 3 + -3 = 0 0 + b = 11.618950039 + -3 b = 11.618950039 + -3 Combine like terms: 11.618950039 + -3 = 8.618950039 b = 8.618950039 Simplifying b = 8.618950039Subproblem 2
b + 3 = -11.618950039 Simplifying b + 3 = -11.618950039 Reorder the terms: 3 + b = -11.618950039 Solving 3 + b = -11.618950039 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = -11.618950039 + -3 Combine like terms: 3 + -3 = 0 0 + b = -11.618950039 + -3 b = -11.618950039 + -3 Combine like terms: -11.618950039 + -3 = -14.618950039 b = -14.618950039 Simplifying b = -14.618950039Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.618950039, -14.618950039}
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