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Simplifying 14469.12 = 2 * 3.14r2 + 2 * 3.14r * 180 Multiply 2 * 3.14 14469.12 = 6.28r2 + 2 * 3.14r * 180 Reorder the terms for easier multiplication: 14469.12 = 6.28r2 + 2 * 3.14 * 180r Multiply 2 * 3.14 14469.12 = 6.28r2 + 6.28 * 180r Multiply 6.28 * 180 14469.12 = 6.28r2 + 1130.4r Reorder the terms: 14469.12 = 1130.4r + 6.28r2 Solving 14469.12 = 1130.4r + 6.28r2 Solving for variable 'r'. Reorder the terms: 14469.12 + -1130.4r + -6.28r2 = 1130.4r + -1130.4r + 6.28r2 + -6.28r2 Combine like terms: 1130.4r + -1130.4r = 0.0 14469.12 + -1130.4r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2 14469.12 + -1130.4r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 14469.12 + -1130.4r + -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'. -2304 + 180r + r2 = 0 Move the constant term to the right: Add '2304' to each side of the equation. -2304 + 180r + 2304 + r2 = 0 + 2304 Reorder the terms: -2304 + 2304 + 180r + r2 = 0 + 2304 Combine like terms: -2304 + 2304 = 0 0 + 180r + r2 = 0 + 2304 180r + r2 = 0 + 2304 Combine like terms: 0 + 2304 = 2304 180r + r2 = 2304 The r term is 180r. Take half its coefficient (90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. 180r + 8100 + r2 = 2304 + 8100 Reorder the terms: 8100 + 180r + r2 = 2304 + 8100 Combine like terms: 2304 + 8100 = 10404 8100 + 180r + r2 = 10404 Factor a perfect square on the left side: (r + 90)(r + 90) = 10404 Calculate the square root of the right side: 102 Break this problem into two subproblems by setting (r + 90) equal to 102 and -102.Subproblem 1
r + 90 = 102 Simplifying r + 90 = 102 Reorder the terms: 90 + r = 102 Solving 90 + r = 102 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + r = 102 + -90 Combine like terms: 90 + -90 = 0 0 + r = 102 + -90 r = 102 + -90 Combine like terms: 102 + -90 = 12 r = 12 Simplifying r = 12Subproblem 2
r + 90 = -102 Simplifying r + 90 = -102 Reorder the terms: 90 + r = -102 Solving 90 + r = -102 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + r = -102 + -90 Combine like terms: 90 + -90 = 0 0 + r = -102 + -90 r = -102 + -90 Combine like terms: -102 + -90 = -192 r = -192 Simplifying r = -192Solution
The solution to the problem is based on the solutions from the subproblems. r = {12, -192}
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