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Simplifying b2 + -5b + -10 = 0 Reorder the terms: -10 + -5b + b2 = 0 Solving -10 + -5b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -5b + 10 + b2 = 0 + 10 Reorder the terms: -10 + 10 + -5b + b2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -5b + b2 = 0 + 10 -5b + b2 = 0 + 10 Combine like terms: 0 + 10 = 10 -5b + b2 = 10 The b term is -5b. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5b + 6.25 + b2 = 10 + 6.25 Reorder the terms: 6.25 + -5b + b2 = 10 + 6.25 Combine like terms: 10 + 6.25 = 16.25 6.25 + -5b + b2 = 16.25 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (b + -2.5) equal to 4.031128874 and -4.031128874.Subproblem 1
b + -2.5 = 4.031128874 Simplifying b + -2.5 = 4.031128874 Reorder the terms: -2.5 + b = 4.031128874 Solving -2.5 + b = 4.031128874 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = 4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = 4.031128874 + 2.5 b = 4.031128874 + 2.5 Combine like terms: 4.031128874 + 2.5 = 6.531128874 b = 6.531128874 Simplifying b = 6.531128874Subproblem 2
b + -2.5 = -4.031128874 Simplifying b + -2.5 = -4.031128874 Reorder the terms: -2.5 + b = -4.031128874 Solving -2.5 + b = -4.031128874 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = -4.031128874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = -4.031128874 + 2.5 b = -4.031128874 + 2.5 Combine like terms: -4.031128874 + 2.5 = -1.531128874 b = -1.531128874 Simplifying b = -1.531128874Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.531128874, -1.531128874}
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