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Simplifying b2 + 2b = 20 Reorder the terms: 2b + b2 = 20 Solving 2b + b2 = 20 Solving for variable 'b'. Reorder the terms: -20 + 2b + b2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 2b + 20 + b2 = 0 + 20 Reorder the terms: -20 + 20 + 2b + b2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 2b + b2 = 0 + 20 2b + b2 = 0 + 20 Combine like terms: 0 + 20 = 20 2b + b2 = 20 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 = 20 + 1 Reorder the terms: 1 + 2b + b2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + 2b + b2 = 21 Factor a perfect square on the left side: (b + 1)(b + 1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (b + 1) equal to 4.582575695 and -4.582575695.Subproblem 1
b + 1 = 4.582575695 Simplifying b + 1 = 4.582575695 Reorder the terms: 1 + b = 4.582575695 Solving 1 + b = 4.582575695 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 = 4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + b = 4.582575695 + -1 b = 4.582575695 + -1 Combine like terms: 4.582575695 + -1 = 3.582575695 b = 3.582575695 Simplifying b = 3.582575695Subproblem 2
b + 1 = -4.582575695 Simplifying b + 1 = -4.582575695 Reorder the terms: 1 + b = -4.582575695 Solving 1 + b = -4.582575695 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 = -4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + b = -4.582575695 + -1 b = -4.582575695 + -1 Combine like terms: -4.582575695 + -1 = -5.582575695 b = -5.582575695 Simplifying b = -5.582575695Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.582575695, -5.582575695}
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