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Simplifying 17b2 + 16b + 3 = 0 Reorder the terms: 3 + 16b + 17b2 = 0 Solving 3 + 16b + 17b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 0.1764705882 + 0.9411764706b + b2 = 0 Move the constant term to the right: Add '-0.1764705882' to each side of the equation. 0.1764705882 + 0.9411764706b + -0.1764705882 + b2 = 0 + -0.1764705882 Reorder the terms: 0.1764705882 + -0.1764705882 + 0.9411764706b + b2 = 0 + -0.1764705882 Combine like terms: 0.1764705882 + -0.1764705882 = 0.0000000000 0.0000000000 + 0.9411764706b + b2 = 0 + -0.1764705882 0.9411764706b + b2 = 0 + -0.1764705882 Combine like terms: 0 + -0.1764705882 = -0.1764705882 0.9411764706b + b2 = -0.1764705882 The b term is 0.9411764706b. Take half its coefficient (0.4705882353). Square it (0.2214532872) and add it to both sides. Add '0.2214532872' to each side of the equation. 0.9411764706b + 0.2214532872 + b2 = -0.1764705882 + 0.2214532872 Reorder the terms: 0.2214532872 + 0.9411764706b + b2 = -0.1764705882 + 0.2214532872 Combine like terms: -0.1764705882 + 0.2214532872 = 0.044982699 0.2214532872 + 0.9411764706b + b2 = 0.044982699 Factor a perfect square on the left side: (b + 0.4705882353)(b + 0.4705882353) = 0.044982699 Calculate the square root of the right side: 0.212091252 Break this problem into two subproblems by setting (b + 0.4705882353) equal to 0.212091252 and -0.212091252.Subproblem 1
b + 0.4705882353 = 0.212091252 Simplifying b + 0.4705882353 = 0.212091252 Reorder the terms: 0.4705882353 + b = 0.212091252 Solving 0.4705882353 + b = 0.212091252 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.4705882353' to each side of the equation. 0.4705882353 + -0.4705882353 + b = 0.212091252 + -0.4705882353 Combine like terms: 0.4705882353 + -0.4705882353 = 0.0000000000 0.0000000000 + b = 0.212091252 + -0.4705882353 b = 0.212091252 + -0.4705882353 Combine like terms: 0.212091252 + -0.4705882353 = -0.2584969833 b = -0.2584969833 Simplifying b = -0.2584969833Subproblem 2
b + 0.4705882353 = -0.212091252 Simplifying b + 0.4705882353 = -0.212091252 Reorder the terms: 0.4705882353 + b = -0.212091252 Solving 0.4705882353 + b = -0.212091252 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.4705882353' to each side of the equation. 0.4705882353 + -0.4705882353 + b = -0.212091252 + -0.4705882353 Combine like terms: 0.4705882353 + -0.4705882353 = 0.0000000000 0.0000000000 + b = -0.212091252 + -0.4705882353 b = -0.212091252 + -0.4705882353 Combine like terms: -0.212091252 + -0.4705882353 = -0.6826794873 b = -0.6826794873 Simplifying b = -0.6826794873Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.2584969833, -0.6826794873}
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