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Simplifying 0 = b2 + 5b + -26 Reorder the terms: 0 = -26 + 5b + b2 Solving 0 = -26 + 5b + b2 Solving for variable 'b'. Combine like terms: 0 + 26 = 26 26 + -5b + -1b2 = -26 + 5b + b2 + 26 + -5b + -1b2 Reorder the terms: 26 + -5b + -1b2 = -26 + 26 + 5b + -5b + b2 + -1b2 Combine like terms: -26 + 26 = 0 26 + -5b + -1b2 = 0 + 5b + -5b + b2 + -1b2 26 + -5b + -1b2 = 5b + -5b + b2 + -1b2 Combine like terms: 5b + -5b = 0 26 + -5b + -1b2 = 0 + b2 + -1b2 26 + -5b + -1b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 26 + -5b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -26 + 5b + b2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + 5b + 26 + b2 = 0 + 26 Reorder the terms: -26 + 26 + 5b + b2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 5b + b2 = 0 + 26 5b + b2 = 0 + 26 Combine like terms: 0 + 26 = 26 5b + b2 = 26 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 = 26 + 6.25 Reorder the terms: 6.25 + 5b + b2 = 26 + 6.25 Combine like terms: 26 + 6.25 = 32.25 6.25 + 5b + b2 = 32.25 Factor a perfect square on the left side: (b + 2.5)(b + 2.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (b + 2.5) equal to 5.678908346 and -5.678908346.Subproblem 1
b + 2.5 = 5.678908346 Simplifying b + 2.5 = 5.678908346 Reorder the terms: 2.5 + b = 5.678908346 Solving 2.5 + b = 5.678908346 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 = 5.678908346 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 5.678908346 + -2.5 b = 5.678908346 + -2.5 Combine like terms: 5.678908346 + -2.5 = 3.178908346 b = 3.178908346 Simplifying b = 3.178908346Subproblem 2
b + 2.5 = -5.678908346 Simplifying b + 2.5 = -5.678908346 Reorder the terms: 2.5 + b = -5.678908346 Solving 2.5 + b = -5.678908346 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 = -5.678908346 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -5.678908346 + -2.5 b = -5.678908346 + -2.5 Combine like terms: -5.678908346 + -2.5 = -8.178908346 b = -8.178908346 Simplifying b = -8.178908346Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.178908346, -8.178908346}
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