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Simplifying 47533.32 = 2 * 3.14r2 + 2 * 3.14r * 243 Multiply 2 * 3.14 47533.32 = 6.28r2 + 2 * 3.14r * 243 Reorder the terms for easier multiplication: 47533.32 = 6.28r2 + 2 * 3.14 * 243r Multiply 2 * 3.14 47533.32 = 6.28r2 + 6.28 * 243r Multiply 6.28 * 243 47533.32 = 6.28r2 + 1526.04r Reorder the terms: 47533.32 = 1526.04r + 6.28r2 Solving 47533.32 = 1526.04r + 6.28r2 Solving for variable 'r'. Reorder the terms: 47533.32 + -1526.04r + -6.28r2 = 1526.04r + -1526.04r + 6.28r2 + -6.28r2 Combine like terms: 1526.04r + -1526.04r = 0.00 47533.32 + -1526.04r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 47533.32 + -1526.04r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 47533.32 + -1526.04r + -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 + 243r + r2 = 0 Move the constant term to the right: Add '7569' to each side of the equation. -7569 + 243r + 7569 + r2 = 0 + 7569 Reorder the terms: -7569 + 7569 + 243r + r2 = 0 + 7569 Combine like terms: -7569 + 7569 = 0 0 + 243r + r2 = 0 + 7569 243r + r2 = 0 + 7569 Combine like terms: 0 + 7569 = 7569 243r + r2 = 7569 The r term is 243r. Take half its coefficient (121.5). Square it (14762.25) and add it to both sides. Add '14762.25' to each side of the equation. 243r + 14762.25 + r2 = 7569 + 14762.25 Reorder the terms: 14762.25 + 243r + r2 = 7569 + 14762.25 Combine like terms: 7569 + 14762.25 = 22331.25 14762.25 + 243r + r2 = 22331.25 Factor a perfect square on the left side: (r + 121.5)(r + 121.5) = 22331.25 Calculate the square root of the right side: 149.436441339 Break this problem into two subproblems by setting (r + 121.5) equal to 149.436441339 and -149.436441339.Subproblem 1
r + 121.5 = 149.436441339 Simplifying r + 121.5 = 149.436441339 Reorder the terms: 121.5 + r = 149.436441339 Solving 121.5 + r = 149.436441339 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-121.5' to each side of the equation. 121.5 + -121.5 + r = 149.436441339 + -121.5 Combine like terms: 121.5 + -121.5 = 0.0 0.0 + r = 149.436441339 + -121.5 r = 149.436441339 + -121.5 Combine like terms: 149.436441339 + -121.5 = 27.936441339 r = 27.936441339 Simplifying r = 27.936441339Subproblem 2
r + 121.5 = -149.436441339 Simplifying r + 121.5 = -149.436441339 Reorder the terms: 121.5 + r = -149.436441339 Solving 121.5 + r = -149.436441339 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-121.5' to each side of the equation. 121.5 + -121.5 + r = -149.436441339 + -121.5 Combine like terms: 121.5 + -121.5 = 0.0 0.0 + r = -149.436441339 + -121.5 r = -149.436441339 + -121.5 Combine like terms: -149.436441339 + -121.5 = -270.936441339 r = -270.936441339 Simplifying r = -270.936441339Solution
The solution to the problem is based on the solutions from the subproblems. r = {27.936441339, -270.936441339}
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