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Simplifying b2 + 16b = -16 Reorder the terms: 16b + b2 = -16 Solving 16b + b2 = -16 Solving for variable 'b'. Reorder the terms: 16 + 16b + b2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + 16b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 16b + -16 + b2 = 0 + -16 Reorder the terms: 16 + -16 + 16b + b2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 16b + b2 = 0 + -16 16b + b2 = 0 + -16 Combine like terms: 0 + -16 = -16 16b + b2 = -16 The b term is 16b. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16b + 64 + b2 = -16 + 64 Reorder the terms: 64 + 16b + b2 = -16 + 64 Combine like terms: -16 + 64 = 48 64 + 16b + b2 = 48 Factor a perfect square on the left side: (b + 8)(b + 8) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (b + 8) equal to 6.92820323 and -6.92820323.Subproblem 1
b + 8 = 6.92820323 Simplifying b + 8 = 6.92820323 Reorder the terms: 8 + b = 6.92820323 Solving 8 + b = 6.92820323 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + b = 6.92820323 + -8 Combine like terms: 8 + -8 = 0 0 + b = 6.92820323 + -8 b = 6.92820323 + -8 Combine like terms: 6.92820323 + -8 = -1.07179677 b = -1.07179677 Simplifying b = -1.07179677Subproblem 2
b + 8 = -6.92820323 Simplifying b + 8 = -6.92820323 Reorder the terms: 8 + b = -6.92820323 Solving 8 + b = -6.92820323 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + b = -6.92820323 + -8 Combine like terms: 8 + -8 = 0 0 + b = -6.92820323 + -8 b = -6.92820323 + -8 Combine like terms: -6.92820323 + -8 = -14.92820323 b = -14.92820323 Simplifying b = -14.92820323Solution
The solution to the problem is based on the solutions from the subproblems. b = {-1.07179677, -14.92820323}
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