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Simplifying -2b2 + 4 = 8 + -13b Reorder the terms: 4 + -2b2 = 8 + -13b Solving 4 + -2b2 = 8 + -13b Solving for variable 'b'. Reorder the terms: 4 + -8 + 13b + -2b2 = 8 + -13b + -8 + 13b Combine like terms: 4 + -8 = -4 -4 + 13b + -2b2 = 8 + -13b + -8 + 13b Reorder the terms: -4 + 13b + -2b2 = 8 + -8 + -13b + 13b Combine like terms: 8 + -8 = 0 -4 + 13b + -2b2 = 0 + -13b + 13b -4 + 13b + -2b2 = -13b + 13b Combine like terms: -13b + 13b = 0 -4 + 13b + -2b2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2 + -6.5b + b2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6.5b + -2 + b2 = 0 + -2 Reorder the terms: 2 + -2 + -6.5b + b2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6.5b + b2 = 0 + -2 -6.5b + b2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6.5b + b2 = -2 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 = -2 + 10.5625 Reorder the terms: 10.5625 + -6.5b + b2 = -2 + 10.5625 Combine like terms: -2 + 10.5625 = 8.5625 10.5625 + -6.5b + b2 = 8.5625 Factor a perfect square on the left side: (b + -3.25)(b + -3.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (b + -3.25) equal to 2.926174978 and -2.926174978.Subproblem 1
b + -3.25 = 2.926174978 Simplifying b + -3.25 = 2.926174978 Reorder the terms: -3.25 + b = 2.926174978 Solving -3.25 + b = 2.926174978 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 = 2.926174978 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + b = 2.926174978 + 3.25 b = 2.926174978 + 3.25 Combine like terms: 2.926174978 + 3.25 = 6.176174978 b = 6.176174978 Simplifying b = 6.176174978Subproblem 2
b + -3.25 = -2.926174978 Simplifying b + -3.25 = -2.926174978 Reorder the terms: -3.25 + b = -2.926174978 Solving -3.25 + b = -2.926174978 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 = -2.926174978 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + b = -2.926174978 + 3.25 b = -2.926174978 + 3.25 Combine like terms: -2.926174978 + 3.25 = 0.323825022 b = 0.323825022 Simplifying b = 0.323825022Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.176174978, 0.323825022}
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