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Simplifying r2 + -11r + 2 = 0 Reorder the terms: 2 + -11r + r2 = 0 Solving 2 + -11r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -11r + -2 + r2 = 0 + -2 Reorder the terms: 2 + -2 + -11r + r2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -11r + r2 = 0 + -2 -11r + r2 = 0 + -2 Combine like terms: 0 + -2 = -2 -11r + r2 = -2 The r term is -11r. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11r + 30.25 + r2 = -2 + 30.25 Reorder the terms: 30.25 + -11r + r2 = -2 + 30.25 Combine like terms: -2 + 30.25 = 28.25 30.25 + -11r + r2 = 28.25 Factor a perfect square on the left side: (r + -5.5)(r + -5.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (r + -5.5) equal to 5.315072906 and -5.315072906.Subproblem 1
r + -5.5 = 5.315072906 Simplifying r + -5.5 = 5.315072906 Reorder the terms: -5.5 + r = 5.315072906 Solving -5.5 + r = 5.315072906 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + r = 5.315072906 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + r = 5.315072906 + 5.5 r = 5.315072906 + 5.5 Combine like terms: 5.315072906 + 5.5 = 10.815072906 r = 10.815072906 Simplifying r = 10.815072906Subproblem 2
r + -5.5 = -5.315072906 Simplifying r + -5.5 = -5.315072906 Reorder the terms: -5.5 + r = -5.315072906 Solving -5.5 + r = -5.315072906 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + r = -5.315072906 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + r = -5.315072906 + 5.5 r = -5.315072906 + 5.5 Combine like terms: -5.315072906 + 5.5 = 0.184927094 r = 0.184927094 Simplifying r = 0.184927094Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.815072906, 0.184927094}
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