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Simplifying r2 + 18r = 21 Reorder the terms: 18r + r2 = 21 Solving 18r + r2 = 21 Solving for variable 'r'. Reorder the terms: -21 + 18r + r2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 18r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 18r + 21 + r2 = 0 + 21 Reorder the terms: -21 + 21 + 18r + r2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 18r + r2 = 0 + 21 18r + r2 = 0 + 21 Combine like terms: 0 + 21 = 21 18r + r2 = 21 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 = 21 + 81 Reorder the terms: 81 + 18r + r2 = 21 + 81 Combine like terms: 21 + 81 = 102 81 + 18r + r2 = 102 Factor a perfect square on the left side: (r + 9)(r + 9) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (r + 9) equal to 10.099504938 and -10.099504938.Subproblem 1
r + 9 = 10.099504938 Simplifying r + 9 = 10.099504938 Reorder the terms: 9 + r = 10.099504938 Solving 9 + r = 10.099504938 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 = 10.099504938 + -9 Combine like terms: 9 + -9 = 0 0 + r = 10.099504938 + -9 r = 10.099504938 + -9 Combine like terms: 10.099504938 + -9 = 1.099504938 r = 1.099504938 Simplifying r = 1.099504938Subproblem 2
r + 9 = -10.099504938 Simplifying r + 9 = -10.099504938 Reorder the terms: 9 + r = -10.099504938 Solving 9 + r = -10.099504938 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 = -10.099504938 + -9 Combine like terms: 9 + -9 = 0 0 + r = -10.099504938 + -9 r = -10.099504938 + -9 Combine like terms: -10.099504938 + -9 = -19.099504938 r = -19.099504938 Simplifying r = -19.099504938Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.099504938, -19.099504938}
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