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Simplifying 11b2 + -62b + -275 = 0 Reorder the terms: -275 + -62b + 11b2 = 0 Solving -275 + -62b + 11b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -25 + -5.636363636b + b2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -5.636363636b + 25 + b2 = 0 + 25 Reorder the terms: -25 + 25 + -5.636363636b + b2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -5.636363636b + b2 = 0 + 25 -5.636363636b + b2 = 0 + 25 Combine like terms: 0 + 25 = 25 -5.636363636b + b2 = 25 The b term is -5.636363636b. Take half its coefficient (-2.818181818). Square it (7.942148759) and add it to both sides. Add '7.942148759' to each side of the equation. -5.636363636b + 7.942148759 + b2 = 25 + 7.942148759 Reorder the terms: 7.942148759 + -5.636363636b + b2 = 25 + 7.942148759 Combine like terms: 25 + 7.942148759 = 32.942148759 7.942148759 + -5.636363636b + b2 = 32.942148759 Factor a perfect square on the left side: (b + -2.818181818)(b + -2.818181818) = 32.942148759 Calculate the square root of the right side: 5.739525134 Break this problem into two subproblems by setting (b + -2.818181818) equal to 5.739525134 and -5.739525134.Subproblem 1
b + -2.818181818 = 5.739525134 Simplifying b + -2.818181818 = 5.739525134 Reorder the terms: -2.818181818 + b = 5.739525134 Solving -2.818181818 + b = 5.739525134 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.818181818' to each side of the equation. -2.818181818 + 2.818181818 + b = 5.739525134 + 2.818181818 Combine like terms: -2.818181818 + 2.818181818 = 0.000000000 0.000000000 + b = 5.739525134 + 2.818181818 b = 5.739525134 + 2.818181818 Combine like terms: 5.739525134 + 2.818181818 = 8.557706952 b = 8.557706952 Simplifying b = 8.557706952Subproblem 2
b + -2.818181818 = -5.739525134 Simplifying b + -2.818181818 = -5.739525134 Reorder the terms: -2.818181818 + b = -5.739525134 Solving -2.818181818 + b = -5.739525134 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.818181818' to each side of the equation. -2.818181818 + 2.818181818 + b = -5.739525134 + 2.818181818 Combine like terms: -2.818181818 + 2.818181818 = 0.000000000 0.000000000 + b = -5.739525134 + 2.818181818 b = -5.739525134 + 2.818181818 Combine like terms: -5.739525134 + 2.818181818 = -2.921343316 b = -2.921343316 Simplifying b = -2.921343316Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.557706952, -2.921343316}
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