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Simplifying 11b2 + -25b + -96 = 0 Reorder the terms: -96 + -25b + 11b2 = 0 Solving -96 + -25b + 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'. -8.727272727 + -2.272727273b + b2 = 0 Move the constant term to the right: Add '8.727272727' to each side of the equation. -8.727272727 + -2.272727273b + 8.727272727 + b2 = 0 + 8.727272727 Reorder the terms: -8.727272727 + 8.727272727 + -2.272727273b + b2 = 0 + 8.727272727 Combine like terms: -8.727272727 + 8.727272727 = 0.000000000 0.000000000 + -2.272727273b + b2 = 0 + 8.727272727 -2.272727273b + b2 = 0 + 8.727272727 Combine like terms: 0 + 8.727272727 = 8.727272727 -2.272727273b + b2 = 8.727272727 The b term is -2.272727273b. Take half its coefficient (-1.136363637). Square it (1.291322316) and add it to both sides. Add '1.291322316' to each side of the equation. -2.272727273b + 1.291322316 + b2 = 8.727272727 + 1.291322316 Reorder the terms: 1.291322316 + -2.272727273b + b2 = 8.727272727 + 1.291322316 Combine like terms: 8.727272727 + 1.291322316 = 10.018595043 1.291322316 + -2.272727273b + b2 = 10.018595043 Factor a perfect square on the left side: (b + -1.136363637)(b + -1.136363637) = 10.018595043 Calculate the square root of the right side: 3.165216429 Break this problem into two subproblems by setting (b + -1.136363637) equal to 3.165216429 and -3.165216429.Subproblem 1
b + -1.136363637 = 3.165216429 Simplifying b + -1.136363637 = 3.165216429 Reorder the terms: -1.136363637 + b = 3.165216429 Solving -1.136363637 + b = 3.165216429 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.136363637' to each side of the equation. -1.136363637 + 1.136363637 + b = 3.165216429 + 1.136363637 Combine like terms: -1.136363637 + 1.136363637 = 0.000000000 0.000000000 + b = 3.165216429 + 1.136363637 b = 3.165216429 + 1.136363637 Combine like terms: 3.165216429 + 1.136363637 = 4.301580066 b = 4.301580066 Simplifying b = 4.301580066Subproblem 2
b + -1.136363637 = -3.165216429 Simplifying b + -1.136363637 = -3.165216429 Reorder the terms: -1.136363637 + b = -3.165216429 Solving -1.136363637 + b = -3.165216429 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.136363637' to each side of the equation. -1.136363637 + 1.136363637 + b = -3.165216429 + 1.136363637 Combine like terms: -1.136363637 + 1.136363637 = 0.000000000 0.000000000 + b = -3.165216429 + 1.136363637 b = -3.165216429 + 1.136363637 Combine like terms: -3.165216429 + 1.136363637 = -2.028852792 b = -2.028852792 Simplifying b = -2.028852792Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.301580066, -2.028852792}
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