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Simplifying -121b2 + -36b + 36 = 0 Reorder the terms: 36 + -36b + -121b2 = 0 Solving 36 + -36b + -121b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by -121 the coefficient of the squared term: Divide each side by '-121'. -0.2975206612 + 0.2975206612b + b2 = 0 Move the constant term to the right: Add '0.2975206612' to each side of the equation. -0.2975206612 + 0.2975206612b + 0.2975206612 + b2 = 0 + 0.2975206612 Reorder the terms: -0.2975206612 + 0.2975206612 + 0.2975206612b + b2 = 0 + 0.2975206612 Combine like terms: -0.2975206612 + 0.2975206612 = 0.0000000000 0.0000000000 + 0.2975206612b + b2 = 0 + 0.2975206612 0.2975206612b + b2 = 0 + 0.2975206612 Combine like terms: 0 + 0.2975206612 = 0.2975206612 0.2975206612b + b2 = 0.2975206612 The b term is 0.2975206612b. Take half its coefficient (0.1487603306). Square it (0.02212963596) and add it to both sides. Add '0.02212963596' to each side of the equation. 0.2975206612b + 0.02212963596 + b2 = 0.2975206612 + 0.02212963596 Reorder the terms: 0.02212963596 + 0.2975206612b + b2 = 0.2975206612 + 0.02212963596 Combine like terms: 0.2975206612 + 0.02212963596 = 0.31965029716 0.02212963596 + 0.2975206612b + b2 = 0.31965029716 Factor a perfect square on the left side: (b + 0.1487603306)(b + 0.1487603306) = 0.31965029716 Calculate the square root of the right side: 0.565376244 Break this problem into two subproblems by setting (b + 0.1487603306) equal to 0.565376244 and -0.565376244.Subproblem 1
b + 0.1487603306 = 0.565376244 Simplifying b + 0.1487603306 = 0.565376244 Reorder the terms: 0.1487603306 + b = 0.565376244 Solving 0.1487603306 + b = 0.565376244 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1487603306' to each side of the equation. 0.1487603306 + -0.1487603306 + b = 0.565376244 + -0.1487603306 Combine like terms: 0.1487603306 + -0.1487603306 = 0.0000000000 0.0000000000 + b = 0.565376244 + -0.1487603306 b = 0.565376244 + -0.1487603306 Combine like terms: 0.565376244 + -0.1487603306 = 0.4166159134 b = 0.4166159134 Simplifying b = 0.4166159134Subproblem 2
b + 0.1487603306 = -0.565376244 Simplifying b + 0.1487603306 = -0.565376244 Reorder the terms: 0.1487603306 + b = -0.565376244 Solving 0.1487603306 + b = -0.565376244 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1487603306' to each side of the equation. 0.1487603306 + -0.1487603306 + b = -0.565376244 + -0.1487603306 Combine like terms: 0.1487603306 + -0.1487603306 = 0.0000000000 0.0000000000 + b = -0.565376244 + -0.1487603306 b = -0.565376244 + -0.1487603306 Combine like terms: -0.565376244 + -0.1487603306 = -0.7141365746 b = -0.7141365746 Simplifying b = -0.7141365746Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.4166159134, -0.7141365746}
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