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Simplifying r2 + 18r + 31 = 0 Reorder the terms: 31 + 18r + r2 = 0 Solving 31 + 18r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 18r + -31 + r2 = 0 + -31 Reorder the terms: 31 + -31 + 18r + r2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 18r + r2 = 0 + -31 18r + r2 = 0 + -31 Combine like terms: 0 + -31 = -31 18r + r2 = -31 The r term is 18r. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18r + 81 + r2 = -31 + 81 Reorder the terms: 81 + 18r + r2 = -31 + 81 Combine like terms: -31 + 81 = 50 81 + 18r + r2 = 50 Factor a perfect square on the left side: (r + 9)(r + 9) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (r + 9) equal to 7.071067812 and -7.071067812.Subproblem 1
r + 9 = 7.071067812 Simplifying r + 9 = 7.071067812 Reorder the terms: 9 + r = 7.071067812 Solving 9 + r = 7.071067812 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + r = 7.071067812 + -9 Combine like terms: 9 + -9 = 0 0 + r = 7.071067812 + -9 r = 7.071067812 + -9 Combine like terms: 7.071067812 + -9 = -1.928932188 r = -1.928932188 Simplifying r = -1.928932188Subproblem 2
r + 9 = -7.071067812 Simplifying r + 9 = -7.071067812 Reorder the terms: 9 + r = -7.071067812 Solving 9 + r = -7.071067812 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + r = -7.071067812 + -9 Combine like terms: 9 + -9 = 0 0 + r = -7.071067812 + -9 r = -7.071067812 + -9 Combine like terms: -7.071067812 + -9 = -16.071067812 r = -16.071067812 Simplifying r = -16.071067812Solution
The solution to the problem is based on the solutions from the subproblems. r = {-1.928932188, -16.071067812}
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