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Simplifying -1b2 + -10b + 36 = 0 Reorder the terms: 36 + -10b + -1b2 = 0 Solving 36 + -10b + -1b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + 10b + b2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 10b + 36 + b2 = 0 + 36 Reorder the terms: -36 + 36 + 10b + b2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 10b + b2 = 0 + 36 10b + b2 = 0 + 36 Combine like terms: 0 + 36 = 36 10b + b2 = 36 The b term is 10b. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10b + 25 + b2 = 36 + 25 Reorder the terms: 25 + 10b + b2 = 36 + 25 Combine like terms: 36 + 25 = 61 25 + 10b + b2 = 61 Factor a perfect square on the left side: (b + 5)(b + 5) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (b + 5) equal to 7.810249676 and -7.810249676.Subproblem 1
b + 5 = 7.810249676 Simplifying b + 5 = 7.810249676 Reorder the terms: 5 + b = 7.810249676 Solving 5 + b = 7.810249676 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = 7.810249676 + -5 Combine like terms: 5 + -5 = 0 0 + b = 7.810249676 + -5 b = 7.810249676 + -5 Combine like terms: 7.810249676 + -5 = 2.810249676 b = 2.810249676 Simplifying b = 2.810249676Subproblem 2
b + 5 = -7.810249676 Simplifying b + 5 = -7.810249676 Reorder the terms: 5 + b = -7.810249676 Solving 5 + b = -7.810249676 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = -7.810249676 + -5 Combine like terms: 5 + -5 = 0 0 + b = -7.810249676 + -5 b = -7.810249676 + -5 Combine like terms: -7.810249676 + -5 = -12.810249676 b = -12.810249676 Simplifying b = -12.810249676Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.810249676, -12.810249676}
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