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Simplifying 47533.32 = 2 * 3.14r * r + 2 * 3.14r * 232 Multiply 2 * 3.14 47533.32 = 6.28r * r + 2 * 3.14r * 232 Multiply r * r 47533.32 = 6.28r2 + 2 * 3.14r * 232 Reorder the terms for easier multiplication: 47533.32 = 6.28r2 + 2 * 3.14 * 232r Multiply 2 * 3.14 47533.32 = 6.28r2 + 6.28 * 232r Multiply 6.28 * 232 47533.32 = 6.28r2 + 1456.96r Reorder the terms: 47533.32 = 1456.96r + 6.28r2 Solving 47533.32 = 1456.96r + 6.28r2 Solving for variable 'r'. Reorder the terms: 47533.32 + -1456.96r + -6.28r2 = 1456.96r + -1456.96r + 6.28r2 + -6.28r2 Combine like terms: 1456.96r + -1456.96r = 0.00 47533.32 + -1456.96r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 47533.32 + -1456.96r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 47533.32 + -1456.96r + -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'. -7569 + 232r + r2 = 0 Move the constant term to the right: Add '7569' to each side of the equation. -7569 + 232r + 7569 + r2 = 0 + 7569 Reorder the terms: -7569 + 7569 + 232r + r2 = 0 + 7569 Combine like terms: -7569 + 7569 = 0 0 + 232r + r2 = 0 + 7569 232r + r2 = 0 + 7569 Combine like terms: 0 + 7569 = 7569 232r + r2 = 7569 The r term is 232r. Take half its coefficient (116). Square it (13456) and add it to both sides. Add '13456' to each side of the equation. 232r + 13456 + r2 = 7569 + 13456 Reorder the terms: 13456 + 232r + r2 = 7569 + 13456 Combine like terms: 7569 + 13456 = 21025 13456 + 232r + r2 = 21025 Factor a perfect square on the left side: (r + 116)(r + 116) = 21025 Calculate the square root of the right side: 145 Break this problem into two subproblems by setting (r + 116) equal to 145 and -145.Subproblem 1
r + 116 = 145 Simplifying r + 116 = 145 Reorder the terms: 116 + r = 145 Solving 116 + r = 145 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-116' to each side of the equation. 116 + -116 + r = 145 + -116 Combine like terms: 116 + -116 = 0 0 + r = 145 + -116 r = 145 + -116 Combine like terms: 145 + -116 = 29 r = 29 Simplifying r = 29Subproblem 2
r + 116 = -145 Simplifying r + 116 = -145 Reorder the terms: 116 + r = -145 Solving 116 + r = -145 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-116' to each side of the equation. 116 + -116 + r = -145 + -116 Combine like terms: 116 + -116 = 0 0 + r = -145 + -116 r = -145 + -116 Combine like terms: -145 + -116 = -261 r = -261 Simplifying r = -261Solution
The solution to the problem is based on the solutions from the subproblems. r = {29, -261}
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