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Simplifying 2b2 + 20b = 91 Reorder the terms: 20b + 2b2 = 91 Solving 20b + 2b2 = 91 Solving for variable 'b'. Reorder the terms: -91 + 20b + 2b2 = 91 + -91 Combine like terms: 91 + -91 = 0 -91 + 20b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -45.5 + 10b + b2 = 0 Move the constant term to the right: Add '45.5' to each side of the equation. -45.5 + 10b + 45.5 + b2 = 0 + 45.5 Reorder the terms: -45.5 + 45.5 + 10b + b2 = 0 + 45.5 Combine like terms: -45.5 + 45.5 = 0.0 0.0 + 10b + b2 = 0 + 45.5 10b + b2 = 0 + 45.5 Combine like terms: 0 + 45.5 = 45.5 10b + b2 = 45.5 The b term is 10b. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10b + 25 + b2 = 45.5 + 25 Reorder the terms: 25 + 10b + b2 = 45.5 + 25 Combine like terms: 45.5 + 25 = 70.5 25 + 10b + b2 = 70.5 Factor a perfect square on the left side: (b + 5)(b + 5) = 70.5 Calculate the square root of the right side: 8.396427812 Break this problem into two subproblems by setting (b + 5) equal to 8.396427812 and -8.396427812.Subproblem 1
b + 5 = 8.396427812 Simplifying b + 5 = 8.396427812 Reorder the terms: 5 + b = 8.396427812 Solving 5 + b = 8.396427812 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = 8.396427812 + -5 Combine like terms: 5 + -5 = 0 0 + b = 8.396427812 + -5 b = 8.396427812 + -5 Combine like terms: 8.396427812 + -5 = 3.396427812 b = 3.396427812 Simplifying b = 3.396427812Subproblem 2
b + 5 = -8.396427812 Simplifying b + 5 = -8.396427812 Reorder the terms: 5 + b = -8.396427812 Solving 5 + b = -8.396427812 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = -8.396427812 + -5 Combine like terms: 5 + -5 = 0 0 + b = -8.396427812 + -5 b = -8.396427812 + -5 Combine like terms: -8.396427812 + -5 = -13.396427812 b = -13.396427812 Simplifying b = -13.396427812Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.396427812, -13.396427812}
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