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Simplifying 2b2 + 2b = 91 Reorder the terms: 2b + 2b2 = 91 Solving 2b + 2b2 = 91 Solving for variable 'b'. Reorder the terms: -91 + 2b + 2b2 = 91 + -91 Combine like terms: 91 + -91 = 0 -91 + 2b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -45.5 + b + b2 = 0 Move the constant term to the right: Add '45.5' to each side of the equation. -45.5 + b + 45.5 + b2 = 0 + 45.5 Reorder the terms: -45.5 + 45.5 + b + b2 = 0 + 45.5 Combine like terms: -45.5 + 45.5 = 0.0 0.0 + b + b2 = 0 + 45.5 b + b2 = 0 + 45.5 Combine like terms: 0 + 45.5 = 45.5 b + b2 = 45.5 The b term is b. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + b2 = 45.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + b2 = 45.5 + 0.25 Combine like terms: 45.5 + 0.25 = 45.75 1.25 + b2 = 45.75 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 45.75 Calculate the square root of the right side: 6.763874629 Break this problem into two subproblems by setting (b + 0.5) equal to 6.763874629 and -6.763874629.Subproblem 1
b + 0.5 = 6.763874629 Simplifying b + 0.5 = 6.763874629 Reorder the terms: 0.5 + b = 6.763874629 Solving 0.5 + b = 6.763874629 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = 6.763874629 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 6.763874629 + -0.5 b = 6.763874629 + -0.5 Combine like terms: 6.763874629 + -0.5 = 6.263874629 b = 6.263874629 Simplifying b = 6.263874629Subproblem 2
b + 0.5 = -6.763874629 Simplifying b + 0.5 = -6.763874629 Reorder the terms: 0.5 + b = -6.763874629 Solving 0.5 + b = -6.763874629 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = -6.763874629 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -6.763874629 + -0.5 b = -6.763874629 + -0.5 Combine like terms: -6.763874629 + -0.5 = -7.263874629 b = -7.263874629 Simplifying b = -7.263874629Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.263874629, -7.263874629}
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