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Simplifying b2 + -8b + -82 = 0 Reorder the terms: -82 + -8b + b2 = 0 Solving -82 + -8b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + -8b + 82 + b2 = 0 + 82 Reorder the terms: -82 + 82 + -8b + b2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + -8b + b2 = 0 + 82 -8b + b2 = 0 + 82 Combine like terms: 0 + 82 = 82 -8b + b2 = 82 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 = 82 + 16 Reorder the terms: 16 + -8b + b2 = 82 + 16 Combine like terms: 82 + 16 = 98 16 + -8b + b2 = 98 Factor a perfect square on the left side: (b + -4)(b + -4) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (b + -4) equal to 9.899494937 and -9.899494937.Subproblem 1
b + -4 = 9.899494937 Simplifying b + -4 = 9.899494937 Reorder the terms: -4 + b = 9.899494937 Solving -4 + b = 9.899494937 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 = 9.899494937 + 4 Combine like terms: -4 + 4 = 0 0 + b = 9.899494937 + 4 b = 9.899494937 + 4 Combine like terms: 9.899494937 + 4 = 13.899494937 b = 13.899494937 Simplifying b = 13.899494937Subproblem 2
b + -4 = -9.899494937 Simplifying b + -4 = -9.899494937 Reorder the terms: -4 + b = -9.899494937 Solving -4 + b = -9.899494937 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 = -9.899494937 + 4 Combine like terms: -4 + 4 = 0 0 + b = -9.899494937 + 4 b = -9.899494937 + 4 Combine like terms: -9.899494937 + 4 = -5.899494937 b = -5.899494937 Simplifying b = -5.899494937Solution
The solution to the problem is based on the solutions from the subproblems. b = {13.899494937, -5.899494937}
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