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Simplifying 2b2 + 13b + 10 = 0 Reorder the terms: 10 + 13b + 2b2 = 0 Solving 10 + 13b + 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'. 5 + 6.5b + b2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 6.5b + -5 + b2 = 0 + -5 Reorder the terms: 5 + -5 + 6.5b + b2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6.5b + b2 = 0 + -5 6.5b + b2 = 0 + -5 Combine like terms: 0 + -5 = -5 6.5b + b2 = -5 The b term is 6.5b. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5b + 10.5625 + b2 = -5 + 10.5625 Reorder the terms: 10.5625 + 6.5b + b2 = -5 + 10.5625 Combine like terms: -5 + 10.5625 = 5.5625 10.5625 + 6.5b + b2 = 5.5625 Factor a perfect square on the left side: (b + 3.25)(b + 3.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (b + 3.25) equal to 2.358495283 and -2.358495283.Subproblem 1
b + 3.25 = 2.358495283 Simplifying b + 3.25 = 2.358495283 Reorder the terms: 3.25 + b = 2.358495283 Solving 3.25 + b = 2.358495283 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + b = 2.358495283 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + b = 2.358495283 + -3.25 b = 2.358495283 + -3.25 Combine like terms: 2.358495283 + -3.25 = -0.891504717 b = -0.891504717 Simplifying b = -0.891504717Subproblem 2
b + 3.25 = -2.358495283 Simplifying b + 3.25 = -2.358495283 Reorder the terms: 3.25 + b = -2.358495283 Solving 3.25 + b = -2.358495283 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + b = -2.358495283 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + b = -2.358495283 + -3.25 b = -2.358495283 + -3.25 Combine like terms: -2.358495283 + -3.25 = -5.608495283 b = -5.608495283 Simplifying b = -5.608495283Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.891504717, -5.608495283}
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