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Simplifying 5651.8116 = (3.14r2) + (3.14r2) + (55.6r * 6.28) Reorder the terms for easier multiplication: 5651.8116 = (3.14r2) + (3.14r2) + (55.6 * 6.28r) Multiply 55.6 * 6.28 5651.8116 = (3.14r2) + (3.14r2) + (349.168r) Reorder the terms: 5651.8116 = (349.168r) + (3.14r2) + (3.14r2) Combine like terms: (3.14r2) + (3.14r2) = 6.28r2 5651.8116 = (349.168r) + 6.28r2 Solving 5651.8116 = (349.168r) + 6.28r2 Solving for variable 'r'. Reorder the terms: 5651.8116 + (-349.168r) + -6.28r2 = (349.168r) + (-349.168r) + 6.28r2 + -6.28r2 Combine like terms: (349.168r) + (-349.168r) = 0.000 5651.8116 + (-349.168r) + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 5651.8116 + (-349.168r) + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 5651.8116 + (-349.168r) + -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'. -899.97 + (55.6r) + r2 = 0 Move the constant term to the right: Add '899.97' to each side of the equation. -899.97 + (55.6r) + 899.97 + r2 = 0 + 899.97 Reorder the terms: -899.97 + 899.97 + (55.6r) + r2 = 0 + 899.97 Combine like terms: -899.97 + 899.97 = 0.00 0.00 + (55.6r) + r2 = 0 + 899.97 (55.6r) + r2 = 0 + 899.97 Combine like terms: 0 + 899.97 = 899.97 (55.6r) + r2 = 899.97 The r term is (55.6r). Take half its coefficient (27.8). Square it (772.84) and add it to both sides. Add '772.84' to each side of the equation. (55.6r) + 772.84 + r2 = 899.97 + 772.84 Reorder the terms: 772.84 + (55.6r) + r2 = 899.97 + 772.84 Combine like terms: 899.97 + 772.84 = 1672.81 772.84 + (55.6r) + r2 = 1672.81 Factor a perfect square on the left side: (r + 27.8)(r + 27.8) = 1672.81 Calculate the square root of the right side: 40.9 Break this problem into two subproblems by setting (r + 27.8) equal to 40.9 and -40.9.Subproblem 1
r + 27.8 = 40.9 Simplifying r + 27.8 = 40.9 Reorder the terms: 27.8 + r = 40.9 Solving 27.8 + r = 40.9 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-27.8' to each side of the equation. 27.8 + -27.8 + r = 40.9 + -27.8 Combine like terms: 27.8 + -27.8 = 0.0 0.0 + r = 40.9 + -27.8 r = 40.9 + -27.8 Combine like terms: 40.9 + -27.8 = 13.1 r = 13.1 Simplifying r = 13.1Subproblem 2
r + 27.8 = -40.9 Simplifying r + 27.8 = -40.9 Reorder the terms: 27.8 + r = -40.9 Solving 27.8 + r = -40.9 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-27.8' to each side of the equation. 27.8 + -27.8 + r = -40.9 + -27.8 Combine like terms: 27.8 + -27.8 = 0.0 0.0 + r = -40.9 + -27.8 r = -40.9 + -27.8 Combine like terms: -40.9 + -27.8 = -68.7 r = -68.7 Simplifying r = -68.7Solution
The solution to the problem is based on the solutions from the subproblems. r = {13.1, -68.7}
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