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Simplifying 2b2 + 10b = 11 Reorder the terms: 10b + 2b2 = 11 Solving 10b + 2b2 = 11 Solving for variable 'b'. Reorder the terms: -11 + 10b + 2b2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 10b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 5b + b2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 5b + 5.5 + b2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 5b + b2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 5b + b2 = 0 + 5.5 5b + b2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 5b + b2 = 5.5 The b term is 5b. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5b + 6.25 + b2 = 5.5 + 6.25 Reorder the terms: 6.25 + 5b + b2 = 5.5 + 6.25 Combine like terms: 5.5 + 6.25 = 11.75 6.25 + 5b + b2 = 11.75 Factor a perfect square on the left side: (b + 2.5)(b + 2.5) = 11.75 Calculate the square root of the right side: 3.4278273 Break this problem into two subproblems by setting (b + 2.5) equal to 3.4278273 and -3.4278273.Subproblem 1
b + 2.5 = 3.4278273 Simplifying b + 2.5 = 3.4278273 Reorder the terms: 2.5 + b = 3.4278273 Solving 2.5 + b = 3.4278273 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = 3.4278273 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 3.4278273 + -2.5 b = 3.4278273 + -2.5 Combine like terms: 3.4278273 + -2.5 = 0.9278273 b = 0.9278273 Simplifying b = 0.9278273Subproblem 2
b + 2.5 = -3.4278273 Simplifying b + 2.5 = -3.4278273 Reorder the terms: 2.5 + b = -3.4278273 Solving 2.5 + b = -3.4278273 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = -3.4278273 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -3.4278273 + -2.5 b = -3.4278273 + -2.5 Combine like terms: -3.4278273 + -2.5 = -5.9278273 b = -5.9278273 Simplifying b = -5.9278273Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.9278273, -5.9278273}
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