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Simplifying b2 + 2b + -76 = 0 Reorder the terms: -76 + 2b + b2 = 0 Solving -76 + 2b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 2b + 76 + b2 = 0 + 76 Reorder the terms: -76 + 76 + 2b + b2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 2b + b2 = 0 + 76 2b + b2 = 0 + 76 Combine like terms: 0 + 76 = 76 2b + b2 = 76 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 = 76 + 1 Reorder the terms: 1 + 2b + b2 = 76 + 1 Combine like terms: 76 + 1 = 77 1 + 2b + b2 = 77 Factor a perfect square on the left side: (b + 1)(b + 1) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (b + 1) equal to 8.774964387 and -8.774964387.Subproblem 1
b + 1 = 8.774964387 Simplifying b + 1 = 8.774964387 Reorder the terms: 1 + b = 8.774964387 Solving 1 + b = 8.774964387 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 = 8.774964387 + -1 Combine like terms: 1 + -1 = 0 0 + b = 8.774964387 + -1 b = 8.774964387 + -1 Combine like terms: 8.774964387 + -1 = 7.774964387 b = 7.774964387 Simplifying b = 7.774964387Subproblem 2
b + 1 = -8.774964387 Simplifying b + 1 = -8.774964387 Reorder the terms: 1 + b = -8.774964387 Solving 1 + b = -8.774964387 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 = -8.774964387 + -1 Combine like terms: 1 + -1 = 0 0 + b = -8.774964387 + -1 b = -8.774964387 + -1 Combine like terms: -8.774964387 + -1 = -9.774964387 b = -9.774964387 Simplifying b = -9.774964387Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.774964387, -9.774964387}
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