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Simplifying 11124.392 = 2 * 3.14r2 + 2 * 3.14r * 87.2 Multiply 2 * 3.14 11124.392 = 6.28r2 + 2 * 3.14r * 87.2 Reorder the terms for easier multiplication: 11124.392 = 6.28r2 + 2 * 3.14 * 87.2r Multiply 2 * 3.14 11124.392 = 6.28r2 + 6.28 * 87.2r Multiply 6.28 * 87.2 11124.392 = 6.28r2 + 547.616r Reorder the terms: 11124.392 = 547.616r + 6.28r2 Solving 11124.392 = 547.616r + 6.28r2 Solving for variable 'r'. Reorder the terms: 11124.392 + -547.616r + -6.28r2 = 547.616r + -547.616r + 6.28r2 + -6.28r2 Combine like terms: 547.616r + -547.616r = 0.000 11124.392 + -547.616r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 11124.392 + -547.616r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 11124.392 + -547.616r + -6.28r2 = 0.00 Begin completing the square. Divide all terms by -6.28 the coefficient of the squared term: Divide each side by '-6.28'. -1771.4 + 87.2r + r2 = 0 Move the constant term to the right: Add '1771.4' to each side of the equation. -1771.4 + 87.2r + 1771.4 + r2 = 0 + 1771.4 Reorder the terms: -1771.4 + 1771.4 + 87.2r + r2 = 0 + 1771.4 Combine like terms: -1771.4 + 1771.4 = 0.0 0.0 + 87.2r + r2 = 0 + 1771.4 87.2r + r2 = 0 + 1771.4 Combine like terms: 0 + 1771.4 = 1771.4 87.2r + r2 = 1771.4 The r term is 87.2r. Take half its coefficient (43.6). Square it (1900.96) and add it to both sides. Add '1900.96' to each side of the equation. 87.2r + 1900.96 + r2 = 1771.4 + 1900.96 Reorder the terms: 1900.96 + 87.2r + r2 = 1771.4 + 1900.96 Combine like terms: 1771.4 + 1900.96 = 3672.36 1900.96 + 87.2r + r2 = 3672.36 Factor a perfect square on the left side: (r + 43.6)(r + 43.6) = 3672.36 Calculate the square root of the right side: 60.6 Break this problem into two subproblems by setting (r + 43.6) equal to 60.6 and -60.6.Subproblem 1
r + 43.6 = 60.6 Simplifying r + 43.6 = 60.6 Reorder the terms: 43.6 + r = 60.6 Solving 43.6 + r = 60.6 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-43.6' to each side of the equation. 43.6 + -43.6 + r = 60.6 + -43.6 Combine like terms: 43.6 + -43.6 = 0.0 0.0 + r = 60.6 + -43.6 r = 60.6 + -43.6 Combine like terms: 60.6 + -43.6 = 17 r = 17 Simplifying r = 17Subproblem 2
r + 43.6 = -60.6 Simplifying r + 43.6 = -60.6 Reorder the terms: 43.6 + r = -60.6 Solving 43.6 + r = -60.6 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-43.6' to each side of the equation. 43.6 + -43.6 + r = -60.6 + -43.6 Combine like terms: 43.6 + -43.6 = 0.0 0.0 + r = -60.6 + -43.6 r = -60.6 + -43.6 Combine like terms: -60.6 + -43.6 = -104.2 r = -104.2 Simplifying r = -104.2Solution
The solution to the problem is based on the solutions from the subproblems. r = {17, -104.2}
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