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Simplifying b2 + 19b + 41 = 0 Reorder the terms: 41 + 19b + b2 = 0 Solving 41 + 19b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 19b + -41 + b2 = 0 + -41 Reorder the terms: 41 + -41 + 19b + b2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 19b + b2 = 0 + -41 19b + b2 = 0 + -41 Combine like terms: 0 + -41 = -41 19b + b2 = -41 The b term is 19b. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19b + 90.25 + b2 = -41 + 90.25 Reorder the terms: 90.25 + 19b + b2 = -41 + 90.25 Combine like terms: -41 + 90.25 = 49.25 90.25 + 19b + b2 = 49.25 Factor a perfect square on the left side: (b + 9.5)(b + 9.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (b + 9.5) equal to 7.017834424 and -7.017834424.Subproblem 1
b + 9.5 = 7.017834424 Simplifying b + 9.5 = 7.017834424 Reorder the terms: 9.5 + b = 7.017834424 Solving 9.5 + b = 7.017834424 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + b = 7.017834424 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + b = 7.017834424 + -9.5 b = 7.017834424 + -9.5 Combine like terms: 7.017834424 + -9.5 = -2.482165576 b = -2.482165576 Simplifying b = -2.482165576Subproblem 2
b + 9.5 = -7.017834424 Simplifying b + 9.5 = -7.017834424 Reorder the terms: 9.5 + b = -7.017834424 Solving 9.5 + b = -7.017834424 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + b = -7.017834424 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + b = -7.017834424 + -9.5 b = -7.017834424 + -9.5 Combine like terms: -7.017834424 + -9.5 = -16.517834424 b = -16.517834424 Simplifying b = -16.517834424Solution
The solution to the problem is based on the solutions from the subproblems. b = {-2.482165576, -16.517834424}
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