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Simplifying 3b2 + -15b + -35 = 0 Reorder the terms: -35 + -15b + 3b2 = 0 Solving -35 + -15b + 3b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11.66666667 + -5b + b2 = 0 Move the constant term to the right: Add '11.66666667' to each side of the equation. -11.66666667 + -5b + 11.66666667 + b2 = 0 + 11.66666667 Reorder the terms: -11.66666667 + 11.66666667 + -5b + b2 = 0 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + -5b + b2 = 0 + 11.66666667 -5b + b2 = 0 + 11.66666667 Combine like terms: 0 + 11.66666667 = 11.66666667 -5b + b2 = 11.66666667 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 = 11.66666667 + 6.25 Reorder the terms: 6.25 + -5b + b2 = 11.66666667 + 6.25 Combine like terms: 11.66666667 + 6.25 = 17.91666667 6.25 + -5b + b2 = 17.91666667 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = 17.91666667 Calculate the square root of the right side: 4.232808367 Break this problem into two subproblems by setting (b + -2.5) equal to 4.232808367 and -4.232808367.Subproblem 1
b + -2.5 = 4.232808367 Simplifying b + -2.5 = 4.232808367 Reorder the terms: -2.5 + b = 4.232808367 Solving -2.5 + b = 4.232808367 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 = 4.232808367 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = 4.232808367 + 2.5 b = 4.232808367 + 2.5 Combine like terms: 4.232808367 + 2.5 = 6.732808367 b = 6.732808367 Simplifying b = 6.732808367Subproblem 2
b + -2.5 = -4.232808367 Simplifying b + -2.5 = -4.232808367 Reorder the terms: -2.5 + b = -4.232808367 Solving -2.5 + b = -4.232808367 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 = -4.232808367 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = -4.232808367 + 2.5 b = -4.232808367 + 2.5 Combine like terms: -4.232808367 + 2.5 = -1.732808367 b = -1.732808367 Simplifying b = -1.732808367Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.732808367, -1.732808367}
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