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Simplifying 2b2 + 11b + 8 = 0 Reorder the terms: 8 + 11b + 2b2 = 0 Solving 8 + 11b + 2b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + 5.5b + b2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 5.5b + -4 + b2 = 0 + -4 Reorder the terms: 4 + -4 + 5.5b + b2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5.5b + b2 = 0 + -4 5.5b + b2 = 0 + -4 Combine like terms: 0 + -4 = -4 5.5b + b2 = -4 The b term is 5.5b. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5b + 7.5625 + b2 = -4 + 7.5625 Reorder the terms: 7.5625 + 5.5b + b2 = -4 + 7.5625 Combine like terms: -4 + 7.5625 = 3.5625 7.5625 + 5.5b + b2 = 3.5625 Factor a perfect square on the left side: (b + 2.75)(b + 2.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (b + 2.75) equal to 1.887458609 and -1.887458609.Subproblem 1
b + 2.75 = 1.887458609 Simplifying b + 2.75 = 1.887458609 Reorder the terms: 2.75 + b = 1.887458609 Solving 2.75 + b = 1.887458609 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + b = 1.887458609 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + b = 1.887458609 + -2.75 b = 1.887458609 + -2.75 Combine like terms: 1.887458609 + -2.75 = -0.862541391 b = -0.862541391 Simplifying b = -0.862541391Subproblem 2
b + 2.75 = -1.887458609 Simplifying b + 2.75 = -1.887458609 Reorder the terms: 2.75 + b = -1.887458609 Solving 2.75 + b = -1.887458609 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + b = -1.887458609 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + b = -1.887458609 + -2.75 b = -1.887458609 + -2.75 Combine like terms: -1.887458609 + -2.75 = -4.637458609 b = -4.637458609 Simplifying b = -4.637458609Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.862541391, -4.637458609}
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