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Simplifying 36 = r(18.5 + r) 36 = (18.5 * r + r * r) 36 = (18.5r + r2) Solving 36 = 18.5r + r2 Solving for variable 'r'. Reorder the terms: 36 + -18.5r + -1r2 = 18.5r + -18.5r + r2 + -1r2 Combine like terms: 18.5r + -18.5r = 0.0 36 + -18.5r + -1r2 = 0.0 + r2 + -1r2 36 + -18.5r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 36 + -18.5r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + 18.5r + r2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 18.5r + 36 + r2 = 0 + 36 Reorder the terms: -36 + 36 + 18.5r + r2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 18.5r + r2 = 0 + 36 18.5r + r2 = 0 + 36 Combine like terms: 0 + 36 = 36 18.5r + r2 = 36 The r term is 18.5r. Take half its coefficient (9.25). Square it (85.5625) and add it to both sides. Add '85.5625' to each side of the equation. 18.5r + 85.5625 + r2 = 36 + 85.5625 Reorder the terms: 85.5625 + 18.5r + r2 = 36 + 85.5625 Combine like terms: 36 + 85.5625 = 121.5625 85.5625 + 18.5r + r2 = 121.5625 Factor a perfect square on the left side: (r + 9.25)(r + 9.25) = 121.5625 Calculate the square root of the right side: 11.025538536 Break this problem into two subproblems by setting (r + 9.25) equal to 11.025538536 and -11.025538536.Subproblem 1
r + 9.25 = 11.025538536 Simplifying r + 9.25 = 11.025538536 Reorder the terms: 9.25 + r = 11.025538536 Solving 9.25 + r = 11.025538536 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + r = 11.025538536 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + r = 11.025538536 + -9.25 r = 11.025538536 + -9.25 Combine like terms: 11.025538536 + -9.25 = 1.775538536 r = 1.775538536 Simplifying r = 1.775538536Subproblem 2
r + 9.25 = -11.025538536 Simplifying r + 9.25 = -11.025538536 Reorder the terms: 9.25 + r = -11.025538536 Solving 9.25 + r = -11.025538536 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + r = -11.025538536 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + r = -11.025538536 + -9.25 r = -11.025538536 + -9.25 Combine like terms: -11.025538536 + -9.25 = -20.275538536 r = -20.275538536 Simplifying r = -20.275538536Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.775538536, -20.275538536}
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