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Simplifying -1b2 + -8b + 10 = 0 Reorder the terms: 10 + -8b + -1b2 = 0 Solving 10 + -8b + -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'. -10 + 8b + b2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 8b + 10 + b2 = 0 + 10 Reorder the terms: -10 + 10 + 8b + b2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 8b + b2 = 0 + 10 8b + b2 = 0 + 10 Combine like terms: 0 + 10 = 10 8b + b2 = 10 The b term is 8b. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8b + 16 + b2 = 10 + 16 Reorder the terms: 16 + 8b + b2 = 10 + 16 Combine like terms: 10 + 16 = 26 16 + 8b + b2 = 26 Factor a perfect square on the left side: (b + 4)(b + 4) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (b + 4) equal to 5.099019514 and -5.099019514.Subproblem 1
b + 4 = 5.099019514 Simplifying b + 4 = 5.099019514 Reorder the terms: 4 + b = 5.099019514 Solving 4 + b = 5.099019514 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = 5.099019514 + -4 Combine like terms: 4 + -4 = 0 0 + b = 5.099019514 + -4 b = 5.099019514 + -4 Combine like terms: 5.099019514 + -4 = 1.099019514 b = 1.099019514 Simplifying b = 1.099019514Subproblem 2
b + 4 = -5.099019514 Simplifying b + 4 = -5.099019514 Reorder the terms: 4 + b = -5.099019514 Solving 4 + b = -5.099019514 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + b = -5.099019514 + -4 Combine like terms: 4 + -4 = 0 0 + b = -5.099019514 + -4 b = -5.099019514 + -4 Combine like terms: -5.099019514 + -4 = -9.099019514 b = -9.099019514 Simplifying b = -9.099019514Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.099019514, -9.099019514}
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