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Simplifying r2 + 18r = 11 Reorder the terms: 18r + r2 = 11 Solving 18r + r2 = 11 Solving for variable 'r'. Reorder the terms: -11 + 18r + r2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 18r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 18r + 11 + r2 = 0 + 11 Reorder the terms: -11 + 11 + 18r + r2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 18r + r2 = 0 + 11 18r + r2 = 0 + 11 Combine like terms: 0 + 11 = 11 18r + r2 = 11 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 = 11 + 81 Reorder the terms: 81 + 18r + r2 = 11 + 81 Combine like terms: 11 + 81 = 92 81 + 18r + r2 = 92 Factor a perfect square on the left side: (r + 9)(r + 9) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (r + 9) equal to 9.591663047 and -9.591663047.Subproblem 1
r + 9 = 9.591663047 Simplifying r + 9 = 9.591663047 Reorder the terms: 9 + r = 9.591663047 Solving 9 + r = 9.591663047 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 = 9.591663047 + -9 Combine like terms: 9 + -9 = 0 0 + r = 9.591663047 + -9 r = 9.591663047 + -9 Combine like terms: 9.591663047 + -9 = 0.591663047 r = 0.591663047 Simplifying r = 0.591663047Subproblem 2
r + 9 = -9.591663047 Simplifying r + 9 = -9.591663047 Reorder the terms: 9 + r = -9.591663047 Solving 9 + r = -9.591663047 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 = -9.591663047 + -9 Combine like terms: 9 + -9 = 0 0 + r = -9.591663047 + -9 r = -9.591663047 + -9 Combine like terms: -9.591663047 + -9 = -18.591663047 r = -18.591663047 Simplifying r = -18.591663047Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.591663047, -18.591663047}
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