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Simplifying r2 + 18r + 69 = 31 Reorder the terms: 69 + 18r + r2 = 31 Solving 69 + 18r + r2 = 31 Solving for variable 'r'. Reorder the terms: 69 + -31 + 18r + r2 = 31 + -31 Combine like terms: 69 + -31 = 38 38 + 18r + r2 = 31 + -31 Combine like terms: 31 + -31 = 0 38 + 18r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + 18r + -38 + r2 = 0 + -38 Reorder the terms: 38 + -38 + 18r + r2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + 18r + r2 = 0 + -38 18r + r2 = 0 + -38 Combine like terms: 0 + -38 = -38 18r + r2 = -38 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 = -38 + 81 Reorder the terms: 81 + 18r + r2 = -38 + 81 Combine like terms: -38 + 81 = 43 81 + 18r + r2 = 43 Factor a perfect square on the left side: (r + 9)(r + 9) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (r + 9) equal to 6.557438524 and -6.557438524.Subproblem 1
r + 9 = 6.557438524 Simplifying r + 9 = 6.557438524 Reorder the terms: 9 + r = 6.557438524 Solving 9 + r = 6.557438524 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 = 6.557438524 + -9 Combine like terms: 9 + -9 = 0 0 + r = 6.557438524 + -9 r = 6.557438524 + -9 Combine like terms: 6.557438524 + -9 = -2.442561476 r = -2.442561476 Simplifying r = -2.442561476Subproblem 2
r + 9 = -6.557438524 Simplifying r + 9 = -6.557438524 Reorder the terms: 9 + r = -6.557438524 Solving 9 + r = -6.557438524 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 = -6.557438524 + -9 Combine like terms: 9 + -9 = 0 0 + r = -6.557438524 + -9 r = -6.557438524 + -9 Combine like terms: -6.557438524 + -9 = -15.557438524 r = -15.557438524 Simplifying r = -15.557438524Solution
The solution to the problem is based on the solutions from the subproblems. r = {-2.442561476, -15.557438524}
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