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Simplifying b2 + -61 = 6b Reorder the terms: -61 + b2 = 6b Solving -61 + b2 = 6b Solving for variable 'b'. Reorder the terms: -61 + -6b + b2 = 6b + -6b Combine like terms: 6b + -6b = 0 -61 + -6b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + -6b + 61 + b2 = 0 + 61 Reorder the terms: -61 + 61 + -6b + b2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + -6b + b2 = 0 + 61 -6b + b2 = 0 + 61 Combine like terms: 0 + 61 = 61 -6b + b2 = 61 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 = 61 + 9 Reorder the terms: 9 + -6b + b2 = 61 + 9 Combine like terms: 61 + 9 = 70 9 + -6b + b2 = 70 Factor a perfect square on the left side: (b + -3)(b + -3) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (b + -3) equal to 8.366600265 and -8.366600265.Subproblem 1
b + -3 = 8.366600265 Simplifying b + -3 = 8.366600265 Reorder the terms: -3 + b = 8.366600265 Solving -3 + b = 8.366600265 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 = 8.366600265 + 3 Combine like terms: -3 + 3 = 0 0 + b = 8.366600265 + 3 b = 8.366600265 + 3 Combine like terms: 8.366600265 + 3 = 11.366600265 b = 11.366600265 Simplifying b = 11.366600265Subproblem 2
b + -3 = -8.366600265 Simplifying b + -3 = -8.366600265 Reorder the terms: -3 + b = -8.366600265 Solving -3 + b = -8.366600265 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 = -8.366600265 + 3 Combine like terms: -3 + 3 = 0 0 + b = -8.366600265 + 3 b = -8.366600265 + 3 Combine like terms: -8.366600265 + 3 = -5.366600265 b = -5.366600265 Simplifying b = -5.366600265Solution
The solution to the problem is based on the solutions from the subproblems. b = {11.366600265, -5.366600265}
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