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Simplifying 965.3616 = 2 * 3.14r2 + 2 * 3.14r Multiply 2 * 3.14 965.3616 = 6.28r2 + 2 * 3.14r Multiply 2 * 3.14 965.3616 = 6.28r2 + 6.28r Reorder the terms: 965.3616 = 6.28r + 6.28r2 Solving 965.3616 = 6.28r + 6.28r2 Solving for variable 'r'. Reorder the terms: 965.3616 + -6.28r + -6.28r2 = 6.28r + -6.28r + 6.28r2 + -6.28r2 Combine like terms: 6.28r + -6.28r = 0.00 965.3616 + -6.28r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 965.3616 + -6.28r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 965.3616 + -6.28r + -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'. -153.72 + r + r2 = 0 Move the constant term to the right: Add '153.72' to each side of the equation. -153.72 + r + 153.72 + r2 = 0 + 153.72 Reorder the terms: -153.72 + 153.72 + r + r2 = 0 + 153.72 Combine like terms: -153.72 + 153.72 = 0.00 0.00 + r + r2 = 0 + 153.72 r + r2 = 0 + 153.72 Combine like terms: 0 + 153.72 = 153.72 r + r2 = 153.72 The r term is r. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + r2 = 153.72 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + r2 = 153.72 + 0.25 Combine like terms: 153.72 + 0.25 = 153.97 1.25 + r2 = 153.97 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = 153.97 Calculate the square root of the right side: 12.408464853 Break this problem into two subproblems by setting (r + 0.5) equal to 12.408464853 and -12.408464853.Subproblem 1
r + 0.5 = 12.408464853 Simplifying r + 0.5 = 12.408464853 Reorder the terms: 0.5 + r = 12.408464853 Solving 0.5 + r = 12.408464853 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 12.408464853 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 12.408464853 + -0.5 r = 12.408464853 + -0.5 Combine like terms: 12.408464853 + -0.5 = 11.908464853 r = 11.908464853 Simplifying r = 11.908464853Subproblem 2
r + 0.5 = -12.408464853 Simplifying r + 0.5 = -12.408464853 Reorder the terms: 0.5 + r = -12.408464853 Solving 0.5 + r = -12.408464853 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -12.408464853 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -12.408464853 + -0.5 r = -12.408464853 + -0.5 Combine like terms: -12.408464853 + -0.5 = -12.908464853 r = -12.908464853 Simplifying r = -12.908464853Solution
The solution to the problem is based on the solutions from the subproblems. r = {11.908464853, -12.908464853}
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