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Simplifying b2 + -1b + -16 = 0 Reorder the terms: -16 + -1b + b2 = 0 Solving -16 + -1b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -1b + 16 + b2 = 0 + 16 Reorder the terms: -16 + 16 + -1b + b2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1b + b2 = 0 + 16 -1b + b2 = 0 + 16 Combine like terms: 0 + 16 = 16 -1b + b2 = 16 The b term is -1b. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1b + 0.25 + b2 = 16 + 0.25 Reorder the terms: 0.25 + -1b + b2 = 16 + 0.25 Combine like terms: 16 + 0.25 = 16.25 0.25 + -1b + b2 = 16.25 Factor a perfect square on the left side: (b + -0.5)(b + -0.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (b + -0.5) equal to 4.031128874 and -4.031128874.Subproblem 1
b + -0.5 = 4.031128874 Simplifying b + -0.5 = 4.031128874 Reorder the terms: -0.5 + b = 4.031128874 Solving -0.5 + b = 4.031128874 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = 4.031128874 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = 4.031128874 + 0.5 b = 4.031128874 + 0.5 Combine like terms: 4.031128874 + 0.5 = 4.531128874 b = 4.531128874 Simplifying b = 4.531128874Subproblem 2
b + -0.5 = -4.031128874 Simplifying b + -0.5 = -4.031128874 Reorder the terms: -0.5 + b = -4.031128874 Solving -0.5 + b = -4.031128874 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = -4.031128874 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = -4.031128874 + 0.5 b = -4.031128874 + 0.5 Combine like terms: -4.031128874 + 0.5 = -3.531128874 b = -3.531128874 Simplifying b = -3.531128874Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.531128874, -3.531128874}
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