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Simplifying b2 + -6b = 8 Reorder the terms: -6b + b2 = 8 Solving -6b + b2 = 8 Solving for variable 'b'. Reorder the terms: -8 + -6b + b2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -6b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -6b + 8 + b2 = 0 + 8 Reorder the terms: -8 + 8 + -6b + b2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6b + b2 = 0 + 8 -6b + b2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6b + b2 = 8 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 = 8 + 9 Reorder the terms: 9 + -6b + b2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + -6b + b2 = 17 Factor a perfect square on the left side: (b + -3)(b + -3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (b + -3) equal to 4.123105626 and -4.123105626.Subproblem 1
b + -3 = 4.123105626 Simplifying b + -3 = 4.123105626 Reorder the terms: -3 + b = 4.123105626 Solving -3 + b = 4.123105626 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 = 4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + b = 4.123105626 + 3 b = 4.123105626 + 3 Combine like terms: 4.123105626 + 3 = 7.123105626 b = 7.123105626 Simplifying b = 7.123105626Subproblem 2
b + -3 = -4.123105626 Simplifying b + -3 = -4.123105626 Reorder the terms: -3 + b = -4.123105626 Solving -3 + b = -4.123105626 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 = -4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + b = -4.123105626 + 3 b = -4.123105626 + 3 Combine like terms: -4.123105626 + 3 = -1.123105626 b = -1.123105626 Simplifying b = -1.123105626Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.123105626, -1.123105626}
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