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Simplifying b2 + 4b = -1 Reorder the terms: 4b + b2 = -1 Solving 4b + b2 = -1 Solving for variable 'b'. Reorder the terms: 1 + 4b + b2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 4b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4b + -1 + b2 = 0 + -1 Reorder the terms: 1 + -1 + 4b + b2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4b + b2 = 0 + -1 4b + b2 = 0 + -1 Combine like terms: 0 + -1 = -1 4b + b2 = -1 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 + 4 Reorder the terms: 4 + 4b + b2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + 4b + b2 = 3 Factor a perfect square on the left side: (b + 2)(b + 2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (b + 2) equal to 1.732050808 and -1.732050808.Subproblem 1
b + 2 = 1.732050808 Simplifying b + 2 = 1.732050808 Reorder the terms: 2 + b = 1.732050808 Solving 2 + b = 1.732050808 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 = 1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + b = 1.732050808 + -2 b = 1.732050808 + -2 Combine like terms: 1.732050808 + -2 = -0.267949192 b = -0.267949192 Simplifying b = -0.267949192Subproblem 2
b + 2 = -1.732050808 Simplifying b + 2 = -1.732050808 Reorder the terms: 2 + b = -1.732050808 Solving 2 + b = -1.732050808 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 = -1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + b = -1.732050808 + -2 b = -1.732050808 + -2 Combine like terms: -1.732050808 + -2 = -3.732050808 b = -3.732050808 Simplifying b = -3.732050808Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.267949192, -3.732050808}
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