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Simplifying 327.816 = 2 * 3.14r2 + 2 * 3.14r * 14.4 Multiply 2 * 3.14 327.816 = 6.28r2 + 2 * 3.14r * 14.4 Reorder the terms for easier multiplication: 327.816 = 6.28r2 + 2 * 3.14 * 14.4r Multiply 2 * 3.14 327.816 = 6.28r2 + 6.28 * 14.4r Multiply 6.28 * 14.4 327.816 = 6.28r2 + 90.432r Reorder the terms: 327.816 = 90.432r + 6.28r2 Solving 327.816 = 90.432r + 6.28r2 Solving for variable 'r'. Reorder the terms: 327.816 + -90.432r + -6.28r2 = 90.432r + -90.432r + 6.28r2 + -6.28r2 Combine like terms: 90.432r + -90.432r = 0.000 327.816 + -90.432r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 327.816 + -90.432r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 327.816 + -90.432r + -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'. -52.2 + 14.4r + r2 = 0 Move the constant term to the right: Add '52.2' to each side of the equation. -52.2 + 14.4r + 52.2 + r2 = 0 + 52.2 Reorder the terms: -52.2 + 52.2 + 14.4r + r2 = 0 + 52.2 Combine like terms: -52.2 + 52.2 = 0.0 0.0 + 14.4r + r2 = 0 + 52.2 14.4r + r2 = 0 + 52.2 Combine like terms: 0 + 52.2 = 52.2 14.4r + r2 = 52.2 The r term is 14.4r. Take half its coefficient (7.2). Square it (51.84) and add it to both sides. Add '51.84' to each side of the equation. 14.4r + 51.84 + r2 = 52.2 + 51.84 Reorder the terms: 51.84 + 14.4r + r2 = 52.2 + 51.84 Combine like terms: 52.2 + 51.84 = 104.04 51.84 + 14.4r + r2 = 104.04 Factor a perfect square on the left side: (r + 7.2)(r + 7.2) = 104.04 Calculate the square root of the right side: 10.2 Break this problem into two subproblems by setting (r + 7.2) equal to 10.2 and -10.2.Subproblem 1
r + 7.2 = 10.2 Simplifying r + 7.2 = 10.2 Reorder the terms: 7.2 + r = 10.2 Solving 7.2 + r = 10.2 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.2' to each side of the equation. 7.2 + -7.2 + r = 10.2 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + r = 10.2 + -7.2 r = 10.2 + -7.2 Combine like terms: 10.2 + -7.2 = 3 r = 3 Simplifying r = 3Subproblem 2
r + 7.2 = -10.2 Simplifying r + 7.2 = -10.2 Reorder the terms: 7.2 + r = -10.2 Solving 7.2 + r = -10.2 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7.2' to each side of the equation. 7.2 + -7.2 + r = -10.2 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + r = -10.2 + -7.2 r = -10.2 + -7.2 Combine like terms: -10.2 + -7.2 = -17.4 r = -17.4 Simplifying r = -17.4Solution
The solution to the problem is based on the solutions from the subproblems. r = {3, -17.4}
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