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Simplifying 7b2 + 2b + -3 = 0 Reorder the terms: -3 + 2b + 7b2 = 0 Solving -3 + 2b + 7b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 0.2857142857b + b2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.2857142857b + 0.4285714286 + b2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 0.2857142857b + b2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 0.2857142857b + b2 = 0 + 0.4285714286 0.2857142857b + b2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 0.2857142857b + b2 = 0.4285714286 The b term is 0.2857142857b. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857b + 0.02040816328 + b2 = 0.4285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857b + b2 = 0.4285714286 + 0.02040816328 Combine like terms: 0.4285714286 + 0.02040816328 = 0.44897959188 0.02040816328 + 0.2857142857b + b2 = 0.44897959188 Factor a perfect square on the left side: (b + 0.1428571429)(b + 0.1428571429) = 0.44897959188 Calculate the square root of the right side: 0.670059394 Break this problem into two subproblems by setting (b + 0.1428571429) equal to 0.670059394 and -0.670059394.Subproblem 1
b + 0.1428571429 = 0.670059394 Simplifying b + 0.1428571429 = 0.670059394 Reorder the terms: 0.1428571429 + b = 0.670059394 Solving 0.1428571429 + b = 0.670059394 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + b = 0.670059394 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + b = 0.670059394 + -0.1428571429 b = 0.670059394 + -0.1428571429 Combine like terms: 0.670059394 + -0.1428571429 = 0.5272022511 b = 0.5272022511 Simplifying b = 0.5272022511Subproblem 2
b + 0.1428571429 = -0.670059394 Simplifying b + 0.1428571429 = -0.670059394 Reorder the terms: 0.1428571429 + b = -0.670059394 Solving 0.1428571429 + b = -0.670059394 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + b = -0.670059394 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + b = -0.670059394 + -0.1428571429 b = -0.670059394 + -0.1428571429 Combine like terms: -0.670059394 + -0.1428571429 = -0.8129165369 b = -0.8129165369 Simplifying b = -0.8129165369Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.5272022511, -0.8129165369}
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