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Simplifying 2(3.14) * r(12) + 2(3.14) * r2 = 1356 Reorder the terms for easier multiplication: 2 * 3.14 * 12r + 2(3.14) * r2 = 1356 Multiply 2 * 3.14 6.28 * 12r + 2(3.14) * r2 = 1356 Multiply 6.28 * 12 75.36r + 2(3.14) * r2 = 1356 Multiply 2 * 3.14 75.36r + 6.28r2 = 1356 Solving 75.36r + 6.28r2 = 1356 Solving for variable 'r'. Reorder the terms: -1356 + 75.36r + 6.28r2 = 1356 + -1356 Combine like terms: 1356 + -1356 = 0 -1356 + 75.36r + 6.28r2 = 0 Begin completing the square. Divide all terms by 6.28 the coefficient of the squared term: Divide each side by '6.28'. -215.9235669 + 12r + r2 = 0 Move the constant term to the right: Add '215.9235669' to each side of the equation. -215.9235669 + 12r + 215.9235669 + r2 = 0 + 215.9235669 Reorder the terms: -215.9235669 + 215.9235669 + 12r + r2 = 0 + 215.9235669 Combine like terms: -215.9235669 + 215.9235669 = 0.0000000 0.0000000 + 12r + r2 = 0 + 215.9235669 12r + r2 = 0 + 215.9235669 Combine like terms: 0 + 215.9235669 = 215.9235669 12r + r2 = 215.9235669 The r term is 12r. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12r + 36 + r2 = 215.9235669 + 36 Reorder the terms: 36 + 12r + r2 = 215.9235669 + 36 Combine like terms: 215.9235669 + 36 = 251.9235669 36 + 12r + r2 = 251.9235669 Factor a perfect square on the left side: (r + 6)(r + 6) = 251.9235669 Calculate the square root of the right side: 15.872100267 Break this problem into two subproblems by setting (r + 6) equal to 15.872100267 and -15.872100267.Subproblem 1
r + 6 = 15.872100267 Simplifying r + 6 = 15.872100267 Reorder the terms: 6 + r = 15.872100267 Solving 6 + r = 15.872100267 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = 15.872100267 + -6 Combine like terms: 6 + -6 = 0 0 + r = 15.872100267 + -6 r = 15.872100267 + -6 Combine like terms: 15.872100267 + -6 = 9.872100267 r = 9.872100267 Simplifying r = 9.872100267Subproblem 2
r + 6 = -15.872100267 Simplifying r + 6 = -15.872100267 Reorder the terms: 6 + r = -15.872100267 Solving 6 + r = -15.872100267 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = -15.872100267 + -6 Combine like terms: 6 + -6 = 0 0 + r = -15.872100267 + -6 r = -15.872100267 + -6 Combine like terms: -15.872100267 + -6 = -21.872100267 r = -21.872100267 Simplifying r = -21.872100267Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.872100267, -21.872100267}
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