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Simplifying b2 + 6b + -69 = 2 Reorder the terms: -69 + 6b + b2 = 2 Solving -69 + 6b + b2 = 2 Solving for variable 'b'. Reorder the terms: -69 + -2 + 6b + b2 = 2 + -2 Combine like terms: -69 + -2 = -71 -71 + 6b + b2 = 2 + -2 Combine like terms: 2 + -2 = 0 -71 + 6b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + 6b + 71 + b2 = 0 + 71 Reorder the terms: -71 + 71 + 6b + b2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + 6b + b2 = 0 + 71 6b + b2 = 0 + 71 Combine like terms: 0 + 71 = 71 6b + b2 = 71 The b term is 6b. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6b + 9 + b2 = 71 + 9 Reorder the terms: 9 + 6b + b2 = 71 + 9 Combine like terms: 71 + 9 = 80 9 + 6b + b2 = 80 Factor a perfect square on the left side: (b + 3)(b + 3) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (b + 3) equal to 8.94427191 and -8.94427191.Subproblem 1
b + 3 = 8.94427191 Simplifying b + 3 = 8.94427191 Reorder the terms: 3 + b = 8.94427191 Solving 3 + b = 8.94427191 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = 8.94427191 + -3 Combine like terms: 3 + -3 = 0 0 + b = 8.94427191 + -3 b = 8.94427191 + -3 Combine like terms: 8.94427191 + -3 = 5.94427191 b = 5.94427191 Simplifying b = 5.94427191Subproblem 2
b + 3 = -8.94427191 Simplifying b + 3 = -8.94427191 Reorder the terms: 3 + b = -8.94427191 Solving 3 + b = -8.94427191 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = -8.94427191 + -3 Combine like terms: 3 + -3 = 0 0 + b = -8.94427191 + -3 b = -8.94427191 + -3 Combine like terms: -8.94427191 + -3 = -11.94427191 b = -11.94427191 Simplifying b = -11.94427191Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.94427191, -11.94427191}
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