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Simplifying 55b2 + -26b + -75 = 0 Reorder the terms: -75 + -26b + 55b2 = 0 Solving -75 + -26b + 55b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 55 the coefficient of the squared term: Divide each side by '55'. -1.363636364 + -0.4727272727b + b2 = 0 Move the constant term to the right: Add '1.363636364' to each side of the equation. -1.363636364 + -0.4727272727b + 1.363636364 + b2 = 0 + 1.363636364 Reorder the terms: -1.363636364 + 1.363636364 + -0.4727272727b + b2 = 0 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + -0.4727272727b + b2 = 0 + 1.363636364 -0.4727272727b + b2 = 0 + 1.363636364 Combine like terms: 0 + 1.363636364 = 1.363636364 -0.4727272727b + b2 = 1.363636364 The b term is -0.4727272727b. Take half its coefficient (-0.2363636364). Square it (0.05586776861) and add it to both sides. Add '0.05586776861' to each side of the equation. -0.4727272727b + 0.05586776861 + b2 = 1.363636364 + 0.05586776861 Reorder the terms: 0.05586776861 + -0.4727272727b + b2 = 1.363636364 + 0.05586776861 Combine like terms: 1.363636364 + 0.05586776861 = 1.41950413261 0.05586776861 + -0.4727272727b + b2 = 1.41950413261 Factor a perfect square on the left side: (b + -0.2363636364)(b + -0.2363636364) = 1.41950413261 Calculate the square root of the right side: 1.191429449 Break this problem into two subproblems by setting (b + -0.2363636364) equal to 1.191429449 and -1.191429449.Subproblem 1
b + -0.2363636364 = 1.191429449 Simplifying b + -0.2363636364 = 1.191429449 Reorder the terms: -0.2363636364 + b = 1.191429449 Solving -0.2363636364 + b = 1.191429449 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2363636364' to each side of the equation. -0.2363636364 + 0.2363636364 + b = 1.191429449 + 0.2363636364 Combine like terms: -0.2363636364 + 0.2363636364 = 0.0000000000 0.0000000000 + b = 1.191429449 + 0.2363636364 b = 1.191429449 + 0.2363636364 Combine like terms: 1.191429449 + 0.2363636364 = 1.4277930854 b = 1.4277930854 Simplifying b = 1.4277930854Subproblem 2
b + -0.2363636364 = -1.191429449 Simplifying b + -0.2363636364 = -1.191429449 Reorder the terms: -0.2363636364 + b = -1.191429449 Solving -0.2363636364 + b = -1.191429449 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2363636364' to each side of the equation. -0.2363636364 + 0.2363636364 + b = -1.191429449 + 0.2363636364 Combine like terms: -0.2363636364 + 0.2363636364 = 0.0000000000 0.0000000000 + b = -1.191429449 + 0.2363636364 b = -1.191429449 + 0.2363636364 Combine like terms: -1.191429449 + 0.2363636364 = -0.9550658126 b = -0.9550658126 Simplifying b = -0.9550658126Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.4277930854, -0.9550658126}
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