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Simplifying (b + 2)(b + 2) = 2.8284 Reorder the terms: (2 + b)(b + 2) = 2.8284 Reorder the terms: (2 + b)(2 + b) = 2.8284 Multiply (2 + b) * (2 + b) (2(2 + b) + b(2 + b)) = 2.8284 ((2 * 2 + b * 2) + b(2 + b)) = 2.8284 ((4 + 2b) + b(2 + b)) = 2.8284 (4 + 2b + (2 * b + b * b)) = 2.8284 (4 + 2b + (2b + b2)) = 2.8284 Combine like terms: 2b + 2b = 4b (4 + 4b + b2) = 2.8284 Solving 4 + 4b + b2 = 2.8284 Solving for variable 'b'. Reorder the terms: 4 + -2.8284 + 4b + b2 = 2.8284 + -2.8284 Combine like terms: 4 + -2.8284 = 1.1716 1.1716 + 4b + b2 = 2.8284 + -2.8284 Combine like terms: 2.8284 + -2.8284 = 0.0000 1.1716 + 4b + b2 = 0.0000 Begin completing the square. Move the constant term to the right: Add '-1.1716' to each side of the equation. 1.1716 + 4b + -1.1716 + b2 = 0.0000 + -1.1716 Reorder the terms: 1.1716 + -1.1716 + 4b + b2 = 0.0000 + -1.1716 Combine like terms: 1.1716 + -1.1716 = 0.0000 0.0000 + 4b + b2 = 0.0000 + -1.1716 4b + b2 = 0.0000 + -1.1716 Combine like terms: 0.0000 + -1.1716 = -1.1716 4b + b2 = -1.1716 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 = -1.1716 + 4 Reorder the terms: 4 + 4b + b2 = -1.1716 + 4 Combine like terms: -1.1716 + 4 = 2.8284 4 + 4b + b2 = 2.8284 Factor a perfect square on the left side: (b + 2)(b + 2) = 2.8284 Calculate the square root of the right side: 1.681784766 Break this problem into two subproblems by setting (b + 2) equal to 1.681784766 and -1.681784766.Subproblem 1
b + 2 = 1.681784766 Simplifying b + 2 = 1.681784766 Reorder the terms: 2 + b = 1.681784766 Solving 2 + b = 1.681784766 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 = 1.681784766 + -2 Combine like terms: 2 + -2 = 0 0 + b = 1.681784766 + -2 b = 1.681784766 + -2 Combine like terms: 1.681784766 + -2 = -0.318215234 b = -0.318215234 Simplifying b = -0.318215234Subproblem 2
b + 2 = -1.681784766 Simplifying b + 2 = -1.681784766 Reorder the terms: 2 + b = -1.681784766 Solving 2 + b = -1.681784766 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 = -1.681784766 + -2 Combine like terms: 2 + -2 = 0 0 + b = -1.681784766 + -2 b = -1.681784766 + -2 Combine like terms: -1.681784766 + -2 = -3.681784766 b = -3.681784766 Simplifying b = -3.681784766Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.318215234, -3.681784766}
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