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Simplifying 25.748 = 2 * 3.14r2 + 2 * 3.14r * 232 Multiply 2 * 3.14 25.748 = 6.28r2 + 2 * 3.14r * 232 Reorder the terms for easier multiplication: 25.748 = 6.28r2 + 2 * 3.14 * 232r Multiply 2 * 3.14 25.748 = 6.28r2 + 6.28 * 232r Multiply 6.28 * 232 25.748 = 6.28r2 + 1456.96r Reorder the terms: 25.748 = 1456.96r + 6.28r2 Solving 25.748 = 1456.96r + 6.28r2 Solving for variable 'r'. Reorder the terms: 25.748 + -1456.96r + -6.28r2 = 1456.96r + -1456.96r + 6.28r2 + -6.28r2 Combine like terms: 1456.96r + -1456.96r = 0.00 25.748 + -1456.96r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 25.748 + -1456.96r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 25.748 + -1456.96r + -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'. -4.1 + 232r + r2 = 0 Move the constant term to the right: Add '4.1' to each side of the equation. -4.1 + 232r + 4.1 + r2 = 0 + 4.1 Reorder the terms: -4.1 + 4.1 + 232r + r2 = 0 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + 232r + r2 = 0 + 4.1 232r + r2 = 0 + 4.1 Combine like terms: 0 + 4.1 = 4.1 232r + r2 = 4.1 The r term is 232r. Take half its coefficient (116). Square it (13456) and add it to both sides. Add '13456' to each side of the equation. 232r + 13456 + r2 = 4.1 + 13456 Reorder the terms: 13456 + 232r + r2 = 4.1 + 13456 Combine like terms: 4.1 + 13456 = 13460.1 13456 + 232r + r2 = 13460.1 Factor a perfect square on the left side: (r + 116)(r + 116) = 13460.1 Calculate the square root of the right side: 116.017671068 Break this problem into two subproblems by setting (r + 116) equal to 116.017671068 and -116.017671068.Subproblem 1
r + 116 = 116.017671068 Simplifying r + 116 = 116.017671068 Reorder the terms: 116 + r = 116.017671068 Solving 116 + r = 116.017671068 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-116' to each side of the equation. 116 + -116 + r = 116.017671068 + -116 Combine like terms: 116 + -116 = 0 0 + r = 116.017671068 + -116 r = 116.017671068 + -116 Combine like terms: 116.017671068 + -116 = 0.017671068 r = 0.017671068 Simplifying r = 0.017671068Subproblem 2
r + 116 = -116.017671068 Simplifying r + 116 = -116.017671068 Reorder the terms: 116 + r = -116.017671068 Solving 116 + r = -116.017671068 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-116' to each side of the equation. 116 + -116 + r = -116.017671068 + -116 Combine like terms: 116 + -116 = 0 0 + r = -116.017671068 + -116 r = -116.017671068 + -116 Combine like terms: -116.017671068 + -116 = -232.017671068 r = -232.017671068 Simplifying r = -232.017671068Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.017671068, -232.017671068}
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