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Simplifying 11b2 + -7b + 1 = 0 Reorder the terms: 1 + -7b + 11b2 = 0 Solving 1 + -7b + 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'. 0.09090909091 + -0.6363636364b + b2 = 0 Move the constant term to the right: Add '-0.09090909091' to each side of the equation. 0.09090909091 + -0.6363636364b + -0.09090909091 + b2 = 0 + -0.09090909091 Reorder the terms: 0.09090909091 + -0.09090909091 + -0.6363636364b + b2 = 0 + -0.09090909091 Combine like terms: 0.09090909091 + -0.09090909091 = 0.00000000000 0.00000000000 + -0.6363636364b + b2 = 0 + -0.09090909091 -0.6363636364b + b2 = 0 + -0.09090909091 Combine like terms: 0 + -0.09090909091 = -0.09090909091 -0.6363636364b + b2 = -0.09090909091 The b term is -0.6363636364b. Take half its coefficient (-0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. -0.6363636364b + 0.1012396694 + b2 = -0.09090909091 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364b + b2 = -0.09090909091 + 0.1012396694 Combine like terms: -0.09090909091 + 0.1012396694 = 0.01033057849 0.1012396694 + -0.6363636364b + b2 = 0.01033057849 Factor a perfect square on the left side: (b + -0.3181818182)(b + -0.3181818182) = 0.01033057849 Calculate the square root of the right side: 0.101639453 Break this problem into two subproblems by setting (b + -0.3181818182) equal to 0.101639453 and -0.101639453.Subproblem 1
b + -0.3181818182 = 0.101639453 Simplifying b + -0.3181818182 = 0.101639453 Reorder the terms: -0.3181818182 + b = 0.101639453 Solving -0.3181818182 + b = 0.101639453 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + b = 0.101639453 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + b = 0.101639453 + 0.3181818182 b = 0.101639453 + 0.3181818182 Combine like terms: 0.101639453 + 0.3181818182 = 0.4198212712 b = 0.4198212712 Simplifying b = 0.4198212712Subproblem 2
b + -0.3181818182 = -0.101639453 Simplifying b + -0.3181818182 = -0.101639453 Reorder the terms: -0.3181818182 + b = -0.101639453 Solving -0.3181818182 + b = -0.101639453 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + b = -0.101639453 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + b = -0.101639453 + 0.3181818182 b = -0.101639453 + 0.3181818182 Combine like terms: -0.101639453 + 0.3181818182 = 0.2165423652 b = 0.2165423652 Simplifying b = 0.2165423652Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.4198212712, 0.2165423652}
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