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Simplifying r2 + r + -28 = 0 Reorder the terms: -28 + r + r2 = 0 Solving -28 + r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + r + 28 + r2 = 0 + 28 Reorder the terms: -28 + 28 + r + r2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + r + r2 = 0 + 28 r + r2 = 0 + 28 Combine like terms: 0 + 28 = 28 r + r2 = 28 The r term is r. 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. r + 0.25 + r2 = 28 + 0.25 Reorder the terms: 0.25 + r + r2 = 28 + 0.25 Combine like terms: 28 + 0.25 = 28.25 0.25 + r + r2 = 28.25 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (r + 0.5) equal to 5.315072906 and -5.315072906.Subproblem 1
r + 0.5 = 5.315072906 Simplifying r + 0.5 = 5.315072906 Reorder the terms: 0.5 + r = 5.315072906 Solving 0.5 + r = 5.315072906 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 5.315072906 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 5.315072906 + -0.5 r = 5.315072906 + -0.5 Combine like terms: 5.315072906 + -0.5 = 4.815072906 r = 4.815072906 Simplifying r = 4.815072906Subproblem 2
r + 0.5 = -5.315072906 Simplifying r + 0.5 = -5.315072906 Reorder the terms: 0.5 + r = -5.315072906 Solving 0.5 + r = -5.315072906 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -5.315072906 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -5.315072906 + -0.5 r = -5.315072906 + -0.5 Combine like terms: -5.315072906 + -0.5 = -5.815072906 r = -5.815072906 Simplifying r = -5.815072906Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.815072906, -5.815072906}
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