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Simplifying b2 + 10b + 20 = 0 Reorder the terms: 20 + 10b + b2 = 0 Solving 20 + 10b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 10b + -20 + b2 = 0 + -20 Reorder the terms: 20 + -20 + 10b + b2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 10b + b2 = 0 + -20 10b + b2 = 0 + -20 Combine like terms: 0 + -20 = -20 10b + b2 = -20 The b term is 10b. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10b + 25 + b2 = -20 + 25 Reorder the terms: 25 + 10b + b2 = -20 + 25 Combine like terms: -20 + 25 = 5 25 + 10b + b2 = 5 Factor a perfect square on the left side: (b + 5)(b + 5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (b + 5) equal to 2.236067978 and -2.236067978.Subproblem 1
b + 5 = 2.236067978 Simplifying b + 5 = 2.236067978 Reorder the terms: 5 + b = 2.236067978 Solving 5 + b = 2.236067978 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = 2.236067978 + -5 Combine like terms: 5 + -5 = 0 0 + b = 2.236067978 + -5 b = 2.236067978 + -5 Combine like terms: 2.236067978 + -5 = -2.763932022 b = -2.763932022 Simplifying b = -2.763932022Subproblem 2
b + 5 = -2.236067978 Simplifying b + 5 = -2.236067978 Reorder the terms: 5 + b = -2.236067978 Solving 5 + b = -2.236067978 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = -2.236067978 + -5 Combine like terms: 5 + -5 = 0 0 + b = -2.236067978 + -5 b = -2.236067978 + -5 Combine like terms: -2.236067978 + -5 = -7.236067978 b = -7.236067978 Simplifying b = -7.236067978Solution
The solution to the problem is based on the solutions from the subproblems. b = {-2.763932022, -7.236067978}
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