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Simplifying b2 + 8b = 7 Reorder the terms: 8b + b2 = 7 Solving 8b + b2 = 7 Solving for variable 'b'. Reorder the terms: -7 + 8b + b2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 8b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 8b + 7 + b2 = 0 + 7 Reorder the terms: -7 + 7 + 8b + b2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 8b + b2 = 0 + 7 8b + b2 = 0 + 7 Combine like terms: 0 + 7 = 7 8b + b2 = 7 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 = 7 + 16 Reorder the terms: 16 + 8b + b2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + 8b + b2 = 23 Factor a perfect square on the left side: (b + 4)(b + 4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (b + 4) equal to 4.795831523 and -4.795831523.Subproblem 1
b + 4 = 4.795831523 Simplifying b + 4 = 4.795831523 Reorder the terms: 4 + b = 4.795831523 Solving 4 + b = 4.795831523 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 = 4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + b = 4.795831523 + -4 b = 4.795831523 + -4 Combine like terms: 4.795831523 + -4 = 0.795831523 b = 0.795831523 Simplifying b = 0.795831523Subproblem 2
b + 4 = -4.795831523 Simplifying b + 4 = -4.795831523 Reorder the terms: 4 + b = -4.795831523 Solving 4 + b = -4.795831523 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 = -4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + b = -4.795831523 + -4 b = -4.795831523 + -4 Combine like terms: -4.795831523 + -4 = -8.795831523 b = -8.795831523 Simplifying b = -8.795831523Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.795831523, -8.795831523}
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