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Simplifying b2 + -2b + -8 = 5 Reorder the terms: -8 + -2b + b2 = 5 Solving -8 + -2b + b2 = 5 Solving for variable 'b'. Reorder the terms: -8 + -5 + -2b + b2 = 5 + -5 Combine like terms: -8 + -5 = -13 -13 + -2b + b2 = 5 + -5 Combine like terms: 5 + -5 = 0 -13 + -2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -2b + 13 + b2 = 0 + 13 Reorder the terms: -13 + 13 + -2b + b2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2b + b2 = 0 + 13 -2b + b2 = 0 + 13 Combine like terms: 0 + 13 = 13 -2b + b2 = 13 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 = 13 + 1 Reorder the terms: 1 + -2b + b2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + -2b + b2 = 14 Factor a perfect square on the left side: (b + -1)(b + -1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (b + -1) equal to 3.741657387 and -3.741657387.Subproblem 1
b + -1 = 3.741657387 Simplifying b + -1 = 3.741657387 Reorder the terms: -1 + b = 3.741657387 Solving -1 + b = 3.741657387 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 = 3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + b = 3.741657387 + 1 b = 3.741657387 + 1 Combine like terms: 3.741657387 + 1 = 4.741657387 b = 4.741657387 Simplifying b = 4.741657387Subproblem 2
b + -1 = -3.741657387 Simplifying b + -1 = -3.741657387 Reorder the terms: -1 + b = -3.741657387 Solving -1 + b = -3.741657387 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 = -3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + b = -3.741657387 + 1 b = -3.741657387 + 1 Combine like terms: -3.741657387 + 1 = -2.741657387 b = -2.741657387 Simplifying b = -2.741657387Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.741657387, -2.741657387}
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