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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 = 94 81 + -18r + r2 = 94 Factor a perfect square on the left side: (r + -9)(r + -9) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (r + -9) equal to 9.695359715 and -9.695359715.Subproblem 1
r + -9 = 9.695359715 Simplifying r + -9 = 9.695359715 Reorder the terms: -9 + r = 9.695359715 Solving -9 + r = 9.695359715 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 = 9.695359715 + 9 Combine like terms: -9 + 9 = 0 0 + r = 9.695359715 + 9 r = 9.695359715 + 9 Combine like terms: 9.695359715 + 9 = 18.695359715 r = 18.695359715 Simplifying r = 18.695359715Subproblem 2
r + -9 = -9.695359715 Simplifying r + -9 = -9.695359715 Reorder the terms: -9 + r = -9.695359715 Solving -9 + r = -9.695359715 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 = -9.695359715 + 9 Combine like terms: -9 + 9 = 0 0 + r = -9.695359715 + 9 r = -9.695359715 + 9 Combine like terms: -9.695359715 + 9 = -0.695359715 r = -0.695359715 Simplifying r = -0.695359715Solution
The solution to the problem is based on the solutions from the subproblems. r = {18.695359715, -0.695359715}
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