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Simplifying r2 + -18r = -13 Reorder the terms: -18r + r2 = -13 Solving -18r + r2 = -13 Solving for variable 'r'. Reorder the terms: 13 + -18r + r2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + -18r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -18r + -13 + r2 = 0 + -13 Reorder the terms: 13 + -13 + -18r + r2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -18r + r2 = 0 + -13 -18r + r2 = 0 + -13 Combine like terms: 0 + -13 = -13 -18r + r2 = -13 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 = -13 + 81 Reorder the terms: 81 + -18r + r2 = -13 + 81 Combine like terms: -13 + 81 = 68 81 + -18r + r2 = 68 Factor a perfect square on the left side: (r + -9)(r + -9) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (r + -9) equal to 8.246211251 and -8.246211251.Subproblem 1
r + -9 = 8.246211251 Simplifying r + -9 = 8.246211251 Reorder the terms: -9 + r = 8.246211251 Solving -9 + r = 8.246211251 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 = 8.246211251 + 9 Combine like terms: -9 + 9 = 0 0 + r = 8.246211251 + 9 r = 8.246211251 + 9 Combine like terms: 8.246211251 + 9 = 17.246211251 r = 17.246211251 Simplifying r = 17.246211251Subproblem 2
r + -9 = -8.246211251 Simplifying r + -9 = -8.246211251 Reorder the terms: -9 + r = -8.246211251 Solving -9 + r = -8.246211251 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 = -8.246211251 + 9 Combine like terms: -9 + 9 = 0 0 + r = -8.246211251 + 9 r = -8.246211251 + 9 Combine like terms: -8.246211251 + 9 = 0.753788749 r = 0.753788749 Simplifying r = 0.753788749Solution
The solution to the problem is based on the solutions from the subproblems. r = {17.246211251, 0.753788749}
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