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Simplifying 98b2 + 1b + -50 = 0 Reorder the terms: -50 + 1b + 98b2 = 0 Solving -50 + 1b + 98b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 98 the coefficient of the squared term: Divide each side by '98'. -0.5102040816 + 0.01020408163b + b2 = 0 Move the constant term to the right: Add '0.5102040816' to each side of the equation. -0.5102040816 + 0.01020408163b + 0.5102040816 + b2 = 0 + 0.5102040816 Reorder the terms: -0.5102040816 + 0.5102040816 + 0.01020408163b + b2 = 0 + 0.5102040816 Combine like terms: -0.5102040816 + 0.5102040816 = 0.0000000000 0.0000000000 + 0.01020408163b + b2 = 0 + 0.5102040816 0.01020408163b + b2 = 0 + 0.5102040816 Combine like terms: 0 + 0.5102040816 = 0.5102040816 0.01020408163b + b2 = 0.5102040816 The b term is 0.01020408163b. Take half its coefficient (0.005102040815). Square it (0.00002603082048) and add it to both sides. Add '0.00002603082048' to each side of the equation. 0.01020408163b + 0.00002603082048 + b2 = 0.5102040816 + 0.00002603082048 Reorder the terms: 0.00002603082048 + 0.01020408163b + b2 = 0.5102040816 + 0.00002603082048 Combine like terms: 0.5102040816 + 0.00002603082048 = 0.51023011242048 0.00002603082048 + 0.01020408163b + b2 = 0.51023011242048 Factor a perfect square on the left side: (b + 0.005102040815)(b + 0.005102040815) = 0.51023011242048 Calculate the square root of the right side: 0.714303936 Break this problem into two subproblems by setting (b + 0.005102040815) equal to 0.714303936 and -0.714303936.Subproblem 1
b + 0.005102040815 = 0.714303936 Simplifying b + 0.005102040815 = 0.714303936 Reorder the terms: 0.005102040815 + b = 0.714303936 Solving 0.005102040815 + b = 0.714303936 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.005102040815' to each side of the equation. 0.005102040815 + -0.005102040815 + b = 0.714303936 + -0.005102040815 Combine like terms: 0.005102040815 + -0.005102040815 = 0.000000000000 0.000000000000 + b = 0.714303936 + -0.005102040815 b = 0.714303936 + -0.005102040815 Combine like terms: 0.714303936 + -0.005102040815 = 0.709201895185 b = 0.709201895185 Simplifying b = 0.709201895185Subproblem 2
b + 0.005102040815 = -0.714303936 Simplifying b + 0.005102040815 = -0.714303936 Reorder the terms: 0.005102040815 + b = -0.714303936 Solving 0.005102040815 + b = -0.714303936 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.005102040815' to each side of the equation. 0.005102040815 + -0.005102040815 + b = -0.714303936 + -0.005102040815 Combine like terms: 0.005102040815 + -0.005102040815 = 0.000000000000 0.000000000000 + b = -0.714303936 + -0.005102040815 b = -0.714303936 + -0.005102040815 Combine like terms: -0.714303936 + -0.005102040815 = -0.719405976815 b = -0.719405976815 Simplifying b = -0.719405976815Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.709201895185, -0.719405976815}
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