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Simplifying b2 + 8b + -23716 = 0 Reorder the terms: -23716 + 8b + b2 = 0 Solving -23716 + 8b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '23716' to each side of the equation. -23716 + 8b + 23716 + b2 = 0 + 23716 Reorder the terms: -23716 + 23716 + 8b + b2 = 0 + 23716 Combine like terms: -23716 + 23716 = 0 0 + 8b + b2 = 0 + 23716 8b + b2 = 0 + 23716 Combine like terms: 0 + 23716 = 23716 8b + b2 = 23716 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 = 23716 + 16 Reorder the terms: 16 + 8b + b2 = 23716 + 16 Combine like terms: 23716 + 16 = 23732 16 + 8b + b2 = 23732 Factor a perfect square on the left side: (b + 4)(b + 4) = 23732 Calculate the square root of the right side: 154.051939293 Break this problem into two subproblems by setting (b + 4) equal to 154.051939293 and -154.051939293.Subproblem 1
b + 4 = 154.051939293 Simplifying b + 4 = 154.051939293 Reorder the terms: 4 + b = 154.051939293 Solving 4 + b = 154.051939293 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 = 154.051939293 + -4 Combine like terms: 4 + -4 = 0 0 + b = 154.051939293 + -4 b = 154.051939293 + -4 Combine like terms: 154.051939293 + -4 = 150.051939293 b = 150.051939293 Simplifying b = 150.051939293Subproblem 2
b + 4 = -154.051939293 Simplifying b + 4 = -154.051939293 Reorder the terms: 4 + b = -154.051939293 Solving 4 + b = -154.051939293 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 = -154.051939293 + -4 Combine like terms: 4 + -4 = 0 0 + b = -154.051939293 + -4 b = -154.051939293 + -4 Combine like terms: -154.051939293 + -4 = -158.051939293 b = -158.051939293 Simplifying b = -158.051939293Solution
The solution to the problem is based on the solutions from the subproblems. b = {150.051939293, -158.051939293}
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