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Simplifying 53b2 + -25b + -58 = 0 Reorder the terms: -58 + -25b + 53b2 = 0 Solving -58 + -25b + 53b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 53 the coefficient of the squared term: Divide each side by '53'. -1.094339623 + -0.4716981132b + b2 = 0 Move the constant term to the right: Add '1.094339623' to each side of the equation. -1.094339623 + -0.4716981132b + 1.094339623 + b2 = 0 + 1.094339623 Reorder the terms: -1.094339623 + 1.094339623 + -0.4716981132b + b2 = 0 + 1.094339623 Combine like terms: -1.094339623 + 1.094339623 = 0.000000000 0.000000000 + -0.4716981132b + b2 = 0 + 1.094339623 -0.4716981132b + b2 = 0 + 1.094339623 Combine like terms: 0 + 1.094339623 = 1.094339623 -0.4716981132b + b2 = 1.094339623 The b term is -0.4716981132b. Take half its coefficient (-0.2358490566). Square it (0.05562477750) and add it to both sides. Add '0.05562477750' to each side of the equation. -0.4716981132b + 0.05562477750 + b2 = 1.094339623 + 0.05562477750 Reorder the terms: 0.05562477750 + -0.4716981132b + b2 = 1.094339623 + 0.05562477750 Combine like terms: 1.094339623 + 0.05562477750 = 1.1499644005 0.05562477750 + -0.4716981132b + b2 = 1.1499644005 Factor a perfect square on the left side: (b + -0.2358490566)(b + -0.2358490566) = 1.1499644005 Calculate the square root of the right side: 1.072363931 Break this problem into two subproblems by setting (b + -0.2358490566) equal to 1.072363931 and -1.072363931.Subproblem 1
b + -0.2358490566 = 1.072363931 Simplifying b + -0.2358490566 = 1.072363931 Reorder the terms: -0.2358490566 + b = 1.072363931 Solving -0.2358490566 + b = 1.072363931 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2358490566' to each side of the equation. -0.2358490566 + 0.2358490566 + b = 1.072363931 + 0.2358490566 Combine like terms: -0.2358490566 + 0.2358490566 = 0.0000000000 0.0000000000 + b = 1.072363931 + 0.2358490566 b = 1.072363931 + 0.2358490566 Combine like terms: 1.072363931 + 0.2358490566 = 1.3082129876 b = 1.3082129876 Simplifying b = 1.3082129876Subproblem 2
b + -0.2358490566 = -1.072363931 Simplifying b + -0.2358490566 = -1.072363931 Reorder the terms: -0.2358490566 + b = -1.072363931 Solving -0.2358490566 + b = -1.072363931 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2358490566' to each side of the equation. -0.2358490566 + 0.2358490566 + b = -1.072363931 + 0.2358490566 Combine like terms: -0.2358490566 + 0.2358490566 = 0.0000000000 0.0000000000 + b = -1.072363931 + 0.2358490566 b = -1.072363931 + 0.2358490566 Combine like terms: -1.072363931 + 0.2358490566 = -0.8365148744 b = -0.8365148744 Simplifying b = -0.8365148744Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.3082129876, -0.8365148744}
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