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Simplifying b2 + 2b + -5 = 0 Reorder the terms: -5 + 2b + b2 = 0 Solving -5 + 2b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2b + 5 + b2 = 0 + 5 Reorder the terms: -5 + 5 + 2b + b2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2b + b2 = 0 + 5 2b + b2 = 0 + 5 Combine like terms: 0 + 5 = 5 2b + b2 = 5 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 = 5 + 1 Reorder the terms: 1 + 2b + b2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2b + b2 = 6 Factor a perfect square on the left side: (b + 1)(b + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (b + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
b + 1 = 2.449489743 Simplifying b + 1 = 2.449489743 Reorder the terms: 1 + b = 2.449489743 Solving 1 + b = 2.449489743 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 = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + b = 2.449489743 + -1 b = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 b = 1.449489743 Simplifying b = 1.449489743Subproblem 2
b + 1 = -2.449489743 Simplifying b + 1 = -2.449489743 Reorder the terms: 1 + b = -2.449489743 Solving 1 + b = -2.449489743 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 = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + b = -2.449489743 + -1 b = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 b = -3.449489743 Simplifying b = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.449489743, -3.449489743}
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