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Simplifying b2 + 20b = -80 Reorder the terms: 20b + b2 = -80 Solving 20b + b2 = -80 Solving for variable 'b'. Reorder the terms: 80 + 20b + b2 = -80 + 80 Combine like terms: -80 + 80 = 0 80 + 20b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 20b + -80 + b2 = 0 + -80 Reorder the terms: 80 + -80 + 20b + b2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 20b + b2 = 0 + -80 20b + b2 = 0 + -80 Combine like terms: 0 + -80 = -80 20b + b2 = -80 The b term is 20b. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20b + 100 + b2 = -80 + 100 Reorder the terms: 100 + 20b + b2 = -80 + 100 Combine like terms: -80 + 100 = 20 100 + 20b + b2 = 20 Factor a perfect square on the left side: (b + 10)(b + 10) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (b + 10) equal to 4.472135955 and -4.472135955.Subproblem 1
b + 10 = 4.472135955 Simplifying b + 10 = 4.472135955 Reorder the terms: 10 + b = 4.472135955 Solving 10 + b = 4.472135955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + b = 4.472135955 + -10 Combine like terms: 10 + -10 = 0 0 + b = 4.472135955 + -10 b = 4.472135955 + -10 Combine like terms: 4.472135955 + -10 = -5.527864045 b = -5.527864045 Simplifying b = -5.527864045Subproblem 2
b + 10 = -4.472135955 Simplifying b + 10 = -4.472135955 Reorder the terms: 10 + b = -4.472135955 Solving 10 + b = -4.472135955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + b = -4.472135955 + -10 Combine like terms: 10 + -10 = 0 0 + b = -4.472135955 + -10 b = -4.472135955 + -10 Combine like terms: -4.472135955 + -10 = -14.472135955 b = -14.472135955 Simplifying b = -14.472135955Solution
The solution to the problem is based on the solutions from the subproblems. b = {-5.527864045, -14.472135955}
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