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Simplifying b2 = 17 + -2b Solving b2 = 17 + -2b Solving for variable 'b'. Reorder the terms: -17 + 2b + b2 = 17 + -2b + -17 + 2b Reorder the terms: -17 + 2b + b2 = 17 + -17 + -2b + 2b Combine like terms: 17 + -17 = 0 -17 + 2b + b2 = 0 + -2b + 2b -17 + 2b + b2 = -2b + 2b Combine like terms: -2b + 2b = 0 -17 + 2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 2b + 17 + b2 = 0 + 17 Reorder the terms: -17 + 17 + 2b + b2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 2b + b2 = 0 + 17 2b + b2 = 0 + 17 Combine like terms: 0 + 17 = 17 2b + b2 = 17 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 = 17 + 1 Reorder the terms: 1 + 2b + b2 = 17 + 1 Combine like terms: 17 + 1 = 18 1 + 2b + b2 = 18 Factor a perfect square on the left side: (b + 1)(b + 1) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (b + 1) equal to 4.242640687 and -4.242640687.Subproblem 1
b + 1 = 4.242640687 Simplifying b + 1 = 4.242640687 Reorder the terms: 1 + b = 4.242640687 Solving 1 + b = 4.242640687 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 = 4.242640687 + -1 Combine like terms: 1 + -1 = 0 0 + b = 4.242640687 + -1 b = 4.242640687 + -1 Combine like terms: 4.242640687 + -1 = 3.242640687 b = 3.242640687 Simplifying b = 3.242640687Subproblem 2
b + 1 = -4.242640687 Simplifying b + 1 = -4.242640687 Reorder the terms: 1 + b = -4.242640687 Solving 1 + b = -4.242640687 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 = -4.242640687 + -1 Combine like terms: 1 + -1 = 0 0 + b = -4.242640687 + -1 b = -4.242640687 + -1 Combine like terms: -4.242640687 + -1 = -5.242640687 b = -5.242640687 Simplifying b = -5.242640687Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.242640687, -5.242640687}
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