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Simplifying 3040.2736 = 2 * 3.14r2 + 2 * 3.14r * 98.9 Multiply 2 * 3.14 3040.2736 = 6.28r2 + 2 * 3.14r * 98.9 Reorder the terms for easier multiplication: 3040.2736 = 6.28r2 + 2 * 3.14 * 98.9r Multiply 2 * 3.14 3040.2736 = 6.28r2 + 6.28 * 98.9r Multiply 6.28 * 98.9 3040.2736 = 6.28r2 + 621.092r Reorder the terms: 3040.2736 = 621.092r + 6.28r2 Solving 3040.2736 = 621.092r + 6.28r2 Solving for variable 'r'. Reorder the terms: 3040.2736 + -621.092r + -6.28r2 = 621.092r + -621.092r + 6.28r2 + -6.28r2 Combine like terms: 621.092r + -621.092r = 0.000 3040.2736 + -621.092r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 3040.2736 + -621.092r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 3040.2736 + -621.092r + -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'. -484.12 + 98.9r + r2 = 0 Move the constant term to the right: Add '484.12' to each side of the equation. -484.12 + 98.9r + 484.12 + r2 = 0 + 484.12 Reorder the terms: -484.12 + 484.12 + 98.9r + r2 = 0 + 484.12 Combine like terms: -484.12 + 484.12 = 0.00 0.00 + 98.9r + r2 = 0 + 484.12 98.9r + r2 = 0 + 484.12 Combine like terms: 0 + 484.12 = 484.12 98.9r + r2 = 484.12 The r term is 98.9r. Take half its coefficient (49.45). Square it (2445.3025) and add it to both sides. Add '2445.3025' to each side of the equation. 98.9r + 2445.3025 + r2 = 484.12 + 2445.3025 Reorder the terms: 2445.3025 + 98.9r + r2 = 484.12 + 2445.3025 Combine like terms: 484.12 + 2445.3025 = 2929.4225 2445.3025 + 98.9r + r2 = 2929.4225 Factor a perfect square on the left side: (r + 49.45)(r + 49.45) = 2929.4225 Calculate the square root of the right side: 54.124139716 Break this problem into two subproblems by setting (r + 49.45) equal to 54.124139716 and -54.124139716.Subproblem 1
r + 49.45 = 54.124139716 Simplifying r + 49.45 = 54.124139716 Reorder the terms: 49.45 + r = 54.124139716 Solving 49.45 + r = 54.124139716 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-49.45' to each side of the equation. 49.45 + -49.45 + r = 54.124139716 + -49.45 Combine like terms: 49.45 + -49.45 = 0.00 0.00 + r = 54.124139716 + -49.45 r = 54.124139716 + -49.45 Combine like terms: 54.124139716 + -49.45 = 4.674139716 r = 4.674139716 Simplifying r = 4.674139716Subproblem 2
r + 49.45 = -54.124139716 Simplifying r + 49.45 = -54.124139716 Reorder the terms: 49.45 + r = -54.124139716 Solving 49.45 + r = -54.124139716 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-49.45' to each side of the equation. 49.45 + -49.45 + r = -54.124139716 + -49.45 Combine like terms: 49.45 + -49.45 = 0.00 0.00 + r = -54.124139716 + -49.45 r = -54.124139716 + -49.45 Combine like terms: -54.124139716 + -49.45 = -103.574139716 r = -103.574139716 Simplifying r = -103.574139716Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.674139716, -103.574139716}
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