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Simplifying b2 + -2b + 1 = 5 Reorder the terms: 1 + -2b + b2 = 5 Solving 1 + -2b + b2 = 5 Solving for variable 'b'. Reorder the terms: 1 + -5 + -2b + b2 = 5 + -5 Combine like terms: 1 + -5 = -4 -4 + -2b + b2 = 5 + -5 Combine like terms: 5 + -5 = 0 -4 + -2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -2b + 4 + b2 = 0 + 4 Reorder the terms: -4 + 4 + -2b + b2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2b + b2 = 0 + 4 -2b + b2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2b + b2 = 4 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 = 4 + 1 Reorder the terms: 1 + -2b + b2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + -2b + b2 = 5 Factor a perfect square on the left side: (b + -1)(b + -1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (b + -1) equal to 2.236067978 and -2.236067978.Subproblem 1
b + -1 = 2.236067978 Simplifying b + -1 = 2.236067978 Reorder the terms: -1 + b = 2.236067978 Solving -1 + b = 2.236067978 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 = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + b = 2.236067978 + 1 b = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 b = 3.236067978 Simplifying b = 3.236067978Subproblem 2
b + -1 = -2.236067978 Simplifying b + -1 = -2.236067978 Reorder the terms: -1 + b = -2.236067978 Solving -1 + b = -2.236067978 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 = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + b = -2.236067978 + 1 b = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 b = -1.236067978 Simplifying b = -1.236067978Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.236067978, -1.236067978}
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