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Simplifying (4 + b) * b = 16 Reorder the terms for easier multiplication: b(4 + b) = 16 (4 * b + b * b) = 16 (4b + b2) = 16 Solving 4b + b2 = 16 Solving for variable 'b'. Reorder the terms: -16 + 4b + b2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 4b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 4b + 16 + b2 = 0 + 16 Reorder the terms: -16 + 16 + 4b + b2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 4b + b2 = 0 + 16 4b + b2 = 0 + 16 Combine like terms: 0 + 16 = 16 4b + b2 = 16 The b term is 4b. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4b + 4 + b2 = 16 + 4 Reorder the terms: 4 + 4b + b2 = 16 + 4 Combine like terms: 16 + 4 = 20 4 + 4b + b2 = 20 Factor a perfect square on the left side: (b + 2)(b + 2) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (b + 2) equal to 4.472135955 and -4.472135955.Subproblem 1
b + 2 = 4.472135955 Simplifying b + 2 = 4.472135955 Reorder the terms: 2 + b = 4.472135955 Solving 2 + b = 4.472135955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = 4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + b = 4.472135955 + -2 b = 4.472135955 + -2 Combine like terms: 4.472135955 + -2 = 2.472135955 b = 2.472135955 Simplifying b = 2.472135955Subproblem 2
b + 2 = -4.472135955 Simplifying b + 2 = -4.472135955 Reorder the terms: 2 + b = -4.472135955 Solving 2 + b = -4.472135955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + b = -4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + b = -4.472135955 + -2 b = -4.472135955 + -2 Combine like terms: -4.472135955 + -2 = -6.472135955 b = -6.472135955 Simplifying b = -6.472135955Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.472135955, -6.472135955}
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