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Simplifying 9b(2 + b) = 36 (2 * 9b + b * 9b) = 36 (18b + 9b2) = 36 Solving 18b + 9b2 = 36 Solving for variable 'b'. Reorder the terms: -36 + 18b + 9b2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 18b + 9b2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-4 + 2b + b2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-4 + 2b + b2)' equal to zero and attempt to solve: Simplifying -4 + 2b + b2 = 0 Solving -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 = 1.236067978 b = 1.236067978 Simplifying b = 1.236067978Subproblem 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 = -3.236067978 b = -3.236067978 Simplifying b = -3.236067978Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.236067978, -3.236067978}Solution
b = {1.236067978, -3.236067978}
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