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Simplifying b2 + -8b + 14 = 0 Reorder the terms: 14 + -8b + b2 = 0 Solving 14 + -8b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -8b + -14 + b2 = 0 + -14 Reorder the terms: 14 + -14 + -8b + b2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -8b + b2 = 0 + -14 -8b + b2 = 0 + -14 Combine like terms: 0 + -14 = -14 -8b + b2 = -14 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 = -14 + 16 Reorder the terms: 16 + -8b + b2 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + -8b + b2 = 2 Factor a perfect square on the left side: (b + -4)(b + -4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (b + -4) equal to 1.414213562 and -1.414213562.Subproblem 1
b + -4 = 1.414213562 Simplifying b + -4 = 1.414213562 Reorder the terms: -4 + b = 1.414213562 Solving -4 + b = 1.414213562 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 = 1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + b = 1.414213562 + 4 b = 1.414213562 + 4 Combine like terms: 1.414213562 + 4 = 5.414213562 b = 5.414213562 Simplifying b = 5.414213562Subproblem 2
b + -4 = -1.414213562 Simplifying b + -4 = -1.414213562 Reorder the terms: -4 + b = -1.414213562 Solving -4 + b = -1.414213562 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 = -1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + b = -1.414213562 + 4 b = -1.414213562 + 4 Combine like terms: -1.414213562 + 4 = 2.585786438 b = 2.585786438 Simplifying b = 2.585786438Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.414213562, 2.585786438}
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