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Simplifying 5b2 + -7b + 1 = 0 Reorder the terms: 1 + -7b + 5b2 = 0 Solving 1 + -7b + 5b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -1.4b + b2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.4b + -0.2 + b2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.4b + b2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.4b + b2 = 0 + -0.2 -1.4b + b2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.4b + b2 = -0.2 The b term is -1.4b. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4b + 0.49 + b2 = -0.2 + 0.49 Reorder the terms: 0.49 + -1.4b + b2 = -0.2 + 0.49 Combine like terms: -0.2 + 0.49 = 0.29 0.49 + -1.4b + b2 = 0.29 Factor a perfect square on the left side: (b + -0.7)(b + -0.7) = 0.29 Calculate the square root of the right side: 0.538516481 Break this problem into two subproblems by setting (b + -0.7) equal to 0.538516481 and -0.538516481.Subproblem 1
b + -0.7 = 0.538516481 Simplifying b + -0.7 = 0.538516481 Reorder the terms: -0.7 + b = 0.538516481 Solving -0.7 + b = 0.538516481 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + b = 0.538516481 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + b = 0.538516481 + 0.7 b = 0.538516481 + 0.7 Combine like terms: 0.538516481 + 0.7 = 1.238516481 b = 1.238516481 Simplifying b = 1.238516481Subproblem 2
b + -0.7 = -0.538516481 Simplifying b + -0.7 = -0.538516481 Reorder the terms: -0.7 + b = -0.538516481 Solving -0.7 + b = -0.538516481 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + b = -0.538516481 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + b = -0.538516481 + 0.7 b = -0.538516481 + 0.7 Combine like terms: -0.538516481 + 0.7 = 0.161483519 b = 0.161483519 Simplifying b = 0.161483519Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.238516481, 0.161483519}
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