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Simplifying b2 + 8b = -5 Reorder the terms: 8b + b2 = -5 Solving 8b + b2 = -5 Solving for variable 'b'. Reorder the terms: 5 + 8b + b2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 8b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 8b + -5 + b2 = 0 + -5 Reorder the terms: 5 + -5 + 8b + b2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8b + b2 = 0 + -5 8b + b2 = 0 + -5 Combine like terms: 0 + -5 = -5 8b + b2 = -5 The b term is 8b. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8b + 16 + b2 = -5 + 16 Reorder the terms: 16 + 8b + b2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + 8b + b2 = 11 Factor a perfect square on the left side: (b + 4)(b + 4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (b + 4) equal to 3.31662479 and -3.31662479.Subproblem 1
b + 4 = 3.31662479 Simplifying b + 4 = 3.31662479 Reorder the terms: 4 + b = 3.31662479 Solving 4 + b = 3.31662479 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = 3.31662479 + -4 Combine like terms: 4 + -4 = 0 0 + b = 3.31662479 + -4 b = 3.31662479 + -4 Combine like terms: 3.31662479 + -4 = -0.68337521 b = -0.68337521 Simplifying b = -0.68337521Subproblem 2
b + 4 = -3.31662479 Simplifying b + 4 = -3.31662479 Reorder the terms: 4 + b = -3.31662479 Solving 4 + b = -3.31662479 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = -3.31662479 + -4 Combine like terms: 4 + -4 = 0 0 + b = -3.31662479 + -4 b = -3.31662479 + -4 Combine like terms: -3.31662479 + -4 = -7.31662479 b = -7.31662479 Simplifying b = -7.31662479Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.68337521, -7.31662479}
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