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Simplifying r2 = 18r + -7 Reorder the terms: r2 = -7 + 18r Solving r2 = -7 + 18r Solving for variable 'r'. Reorder the terms: 7 + -18r + r2 = -7 + 18r + 7 + -18r Reorder the terms: 7 + -18r + r2 = -7 + 7 + 18r + -18r Combine like terms: -7 + 7 = 0 7 + -18r + r2 = 0 + 18r + -18r 7 + -18r + r2 = 18r + -18r Combine like terms: 18r + -18r = 0 7 + -18r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -18r + -7 + r2 = 0 + -7 Reorder the terms: 7 + -7 + -18r + r2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -18r + r2 = 0 + -7 -18r + r2 = 0 + -7 Combine like terms: 0 + -7 = -7 -18r + r2 = -7 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 = -7 + 81 Reorder the terms: 81 + -18r + r2 = -7 + 81 Combine like terms: -7 + 81 = 74 81 + -18r + r2 = 74 Factor a perfect square on the left side: (r + -9)(r + -9) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (r + -9) equal to 8.602325267 and -8.602325267.Subproblem 1
r + -9 = 8.602325267 Simplifying r + -9 = 8.602325267 Reorder the terms: -9 + r = 8.602325267 Solving -9 + r = 8.602325267 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 = 8.602325267 + 9 Combine like terms: -9 + 9 = 0 0 + r = 8.602325267 + 9 r = 8.602325267 + 9 Combine like terms: 8.602325267 + 9 = 17.602325267 r = 17.602325267 Simplifying r = 17.602325267Subproblem 2
r + -9 = -8.602325267 Simplifying r + -9 = -8.602325267 Reorder the terms: -9 + r = -8.602325267 Solving -9 + r = -8.602325267 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 = -8.602325267 + 9 Combine like terms: -9 + 9 = 0 0 + r = -8.602325267 + 9 r = -8.602325267 + 9 Combine like terms: -8.602325267 + 9 = 0.397674733 r = 0.397674733 Simplifying r = 0.397674733Solution
The solution to the problem is based on the solutions from the subproblems. r = {17.602325267, 0.397674733}
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