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Simplifying 4b2 + 20b + 25 = 20 Reorder the terms: 25 + 20b + 4b2 = 20 Solving 25 + 20b + 4b2 = 20 Solving for variable 'b'. Reorder the terms: 25 + -20 + 20b + 4b2 = 20 + -20 Combine like terms: 25 + -20 = 5 5 + 20b + 4b2 = 20 + -20 Combine like terms: 20 + -20 = 0 5 + 20b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 5b + b2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 5b + -1.25 + b2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 5b + b2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 5b + b2 = 0 + -1.25 5b + b2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 5b + b2 = -1.25 The b term is 5b. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5b + 6.25 + b2 = -1.25 + 6.25 Reorder the terms: 6.25 + 5b + b2 = -1.25 + 6.25 Combine like terms: -1.25 + 6.25 = 5 6.25 + 5b + b2 = 5 Factor a perfect square on the left side: (b + 2.5)(b + 2.5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (b + 2.5) equal to 2.236067978 and -2.236067978.Subproblem 1
b + 2.5 = 2.236067978 Simplifying b + 2.5 = 2.236067978 Reorder the terms: 2.5 + b = 2.236067978 Solving 2.5 + b = 2.236067978 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = 2.236067978 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 2.236067978 + -2.5 b = 2.236067978 + -2.5 Combine like terms: 2.236067978 + -2.5 = -0.263932022 b = -0.263932022 Simplifying b = -0.263932022Subproblem 2
b + 2.5 = -2.236067978 Simplifying b + 2.5 = -2.236067978 Reorder the terms: 2.5 + b = -2.236067978 Solving 2.5 + b = -2.236067978 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = -2.236067978 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -2.236067978 + -2.5 b = -2.236067978 + -2.5 Combine like terms: -2.236067978 + -2.5 = -4.736067978 b = -4.736067978 Simplifying b = -4.736067978Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.263932022, -4.736067978}
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