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Simplifying 6b2 + -18 + -95 = -7b Reorder the terms: -18 + -95 + 6b2 = -7b Combine like terms: -18 + -95 = -113 -113 + 6b2 = -7b Solving -113 + 6b2 = -7b Solving for variable 'b'. Reorder the terms: -113 + 7b + 6b2 = -7b + 7b Combine like terms: -7b + 7b = 0 -113 + 7b + 6b2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -18.83333333 + 1.166666667b + b2 = 0 Move the constant term to the right: Add '18.83333333' to each side of the equation. -18.83333333 + 1.166666667b + 18.83333333 + b2 = 0 + 18.83333333 Reorder the terms: -18.83333333 + 18.83333333 + 1.166666667b + b2 = 0 + 18.83333333 Combine like terms: -18.83333333 + 18.83333333 = 0.00000000 0.00000000 + 1.166666667b + b2 = 0 + 18.83333333 1.166666667b + b2 = 0 + 18.83333333 Combine like terms: 0 + 18.83333333 = 18.83333333 1.166666667b + b2 = 18.83333333 The b term is 1.166666667b. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667b + 0.3402777780 + b2 = 18.83333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667b + b2 = 18.83333333 + 0.3402777780 Combine like terms: 18.83333333 + 0.3402777780 = 19.173611108 0.3402777780 + 1.166666667b + b2 = 19.173611108 Factor a perfect square on the left side: (b + 0.5833333335)(b + 0.5833333335) = 19.173611108 Calculate the square root of the right side: 4.378768218 Break this problem into two subproblems by setting (b + 0.5833333335) equal to 4.378768218 and -4.378768218.Subproblem 1
b + 0.5833333335 = 4.378768218 Simplifying b + 0.5833333335 = 4.378768218 Reorder the terms: 0.5833333335 + b = 4.378768218 Solving 0.5833333335 + b = 4.378768218 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + b = 4.378768218 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + b = 4.378768218 + -0.5833333335 b = 4.378768218 + -0.5833333335 Combine like terms: 4.378768218 + -0.5833333335 = 3.7954348845 b = 3.7954348845 Simplifying b = 3.7954348845Subproblem 2
b + 0.5833333335 = -4.378768218 Simplifying b + 0.5833333335 = -4.378768218 Reorder the terms: 0.5833333335 + b = -4.378768218 Solving 0.5833333335 + b = -4.378768218 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + b = -4.378768218 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + b = -4.378768218 + -0.5833333335 b = -4.378768218 + -0.5833333335 Combine like terms: -4.378768218 + -0.5833333335 = -4.9621015515 b = -4.9621015515 Simplifying b = -4.9621015515Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.7954348845, -4.9621015515}
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