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Simplifying 18b2 + 5b + -4 = 0 Reorder the terms: -4 + 5b + 18b2 = 0 Solving -4 + 5b + 18b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2222222222 + 0.2777777778b + b2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2777777778b + 0.2222222222 + b2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 0.2777777778b + b2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 0.2777777778b + b2 = 0 + 0.2222222222 0.2777777778b + b2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 0.2777777778b + b2 = 0.2222222222 The b term is 0.2777777778b. Take half its coefficient (0.1388888889). Square it (0.01929012346) and add it to both sides. Add '0.01929012346' to each side of the equation. 0.2777777778b + 0.01929012346 + b2 = 0.2222222222 + 0.01929012346 Reorder the terms: 0.01929012346 + 0.2777777778b + b2 = 0.2222222222 + 0.01929012346 Combine like terms: 0.2222222222 + 0.01929012346 = 0.24151234566 0.01929012346 + 0.2777777778b + b2 = 0.24151234566 Factor a perfect square on the left side: (b + 0.1388888889)(b + 0.1388888889) = 0.24151234566 Calculate the square root of the right side: 0.491439056 Break this problem into two subproblems by setting (b + 0.1388888889) equal to 0.491439056 and -0.491439056.Subproblem 1
b + 0.1388888889 = 0.491439056 Simplifying b + 0.1388888889 = 0.491439056 Reorder the terms: 0.1388888889 + b = 0.491439056 Solving 0.1388888889 + b = 0.491439056 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.1388888889 + b = 0.491439056 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + b = 0.491439056 + -0.1388888889 b = 0.491439056 + -0.1388888889 Combine like terms: 0.491439056 + -0.1388888889 = 0.3525501671 b = 0.3525501671 Simplifying b = 0.3525501671Subproblem 2
b + 0.1388888889 = -0.491439056 Simplifying b + 0.1388888889 = -0.491439056 Reorder the terms: 0.1388888889 + b = -0.491439056 Solving 0.1388888889 + b = -0.491439056 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.1388888889 + b = -0.491439056 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + b = -0.491439056 + -0.1388888889 b = -0.491439056 + -0.1388888889 Combine like terms: -0.491439056 + -0.1388888889 = -0.6303279449 b = -0.6303279449 Simplifying b = -0.6303279449Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.3525501671, -0.6303279449}
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