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Simplifying b2 + -2b + -41 = 6 Reorder the terms: -41 + -2b + b2 = 6 Solving -41 + -2b + b2 = 6 Solving for variable 'b'. Reorder the terms: -41 + -6 + -2b + b2 = 6 + -6 Combine like terms: -41 + -6 = -47 -47 + -2b + b2 = 6 + -6 Combine like terms: 6 + -6 = 0 -47 + -2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -2b + 47 + b2 = 0 + 47 Reorder the terms: -47 + 47 + -2b + b2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -2b + b2 = 0 + 47 -2b + b2 = 0 + 47 Combine like terms: 0 + 47 = 47 -2b + b2 = 47 The b term is -2b. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2b + 1 + b2 = 47 + 1 Reorder the terms: 1 + -2b + b2 = 47 + 1 Combine like terms: 47 + 1 = 48 1 + -2b + b2 = 48 Factor a perfect square on the left side: (b + -1)(b + -1) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (b + -1) equal to 6.92820323 and -6.92820323.Subproblem 1
b + -1 = 6.92820323 Simplifying b + -1 = 6.92820323 Reorder the terms: -1 + b = 6.92820323 Solving -1 + b = 6.92820323 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 6.92820323 + 1 Combine like terms: -1 + 1 = 0 0 + b = 6.92820323 + 1 b = 6.92820323 + 1 Combine like terms: 6.92820323 + 1 = 7.92820323 b = 7.92820323 Simplifying b = 7.92820323Subproblem 2
b + -1 = -6.92820323 Simplifying b + -1 = -6.92820323 Reorder the terms: -1 + b = -6.92820323 Solving -1 + b = -6.92820323 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -6.92820323 + 1 Combine like terms: -1 + 1 = 0 0 + b = -6.92820323 + 1 b = -6.92820323 + 1 Combine like terms: -6.92820323 + 1 = -5.92820323 b = -5.92820323 Simplifying b = -5.92820323Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.92820323, -5.92820323}
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