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Simplifying (4b2 + 8b) + (2b + -15) = 0 Reorder the terms: (8b + 4b2) + (2b + -15) = 0 Remove parenthesis around (8b + 4b2) 8b + 4b2 + (2b + -15) = 0 Reorder the terms: 8b + 4b2 + (-15 + 2b) = 0 Remove parenthesis around (-15 + 2b) 8b + 4b2 + -15 + 2b = 0 Reorder the terms: -15 + 8b + 2b + 4b2 = 0 Combine like terms: 8b + 2b = 10b -15 + 10b + 4b2 = 0 Solving -15 + 10b + 4b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 2.5b + b2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 2.5b + 3.75 + b2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 2.5b + b2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 2.5b + b2 = 0 + 3.75 2.5b + b2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 2.5b + b2 = 3.75 The b term is 2.5b. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5b + 1.5625 + b2 = 3.75 + 1.5625 Reorder the terms: 1.5625 + 2.5b + b2 = 3.75 + 1.5625 Combine like terms: 3.75 + 1.5625 = 5.3125 1.5625 + 2.5b + b2 = 5.3125 Factor a perfect square on the left side: (b + 1.25)(b + 1.25) = 5.3125 Calculate the square root of the right side: 2.304886114 Break this problem into two subproblems by setting (b + 1.25) equal to 2.304886114 and -2.304886114.Subproblem 1
b + 1.25 = 2.304886114 Simplifying b + 1.25 = 2.304886114 Reorder the terms: 1.25 + b = 2.304886114 Solving 1.25 + b = 2.304886114 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + b = 2.304886114 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + b = 2.304886114 + -1.25 b = 2.304886114 + -1.25 Combine like terms: 2.304886114 + -1.25 = 1.054886114 b = 1.054886114 Simplifying b = 1.054886114Subproblem 2
b + 1.25 = -2.304886114 Simplifying b + 1.25 = -2.304886114 Reorder the terms: 1.25 + b = -2.304886114 Solving 1.25 + b = -2.304886114 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + b = -2.304886114 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + b = -2.304886114 + -1.25 b = -2.304886114 + -1.25 Combine like terms: -2.304886114 + -1.25 = -3.554886114 b = -3.554886114 Simplifying b = -3.554886114Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.054886114, -3.554886114}
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