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Simplifying 56611.328 = 6.28r2 + 1514.736r Reorder the terms: 56611.328 = 1514.736r + 6.28r2 Solving 56611.328 = 1514.736r + 6.28r2 Solving for variable 'r'. Reorder the terms: 56611.328 + -1514.736r + -6.28r2 = 1514.736r + -1514.736r + 6.28r2 + -6.28r2 Combine like terms: 1514.736r + -1514.736r = 0.000 56611.328 + -1514.736r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 56611.328 + -1514.736r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 56611.328 + -1514.736r + -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'. -9014.542675 + 241.2r + r2 = 0 Move the constant term to the right: Add '9014.542675' to each side of the equation. -9014.542675 + 241.2r + 9014.542675 + r2 = 0 + 9014.542675 Reorder the terms: -9014.542675 + 9014.542675 + 241.2r + r2 = 0 + 9014.542675 Combine like terms: -9014.542675 + 9014.542675 = 0.000000 0.000000 + 241.2r + r2 = 0 + 9014.542675 241.2r + r2 = 0 + 9014.542675 Combine like terms: 0 + 9014.542675 = 9014.542675 241.2r + r2 = 9014.542675 The r term is 241.2r. Take half its coefficient (120.6). Square it (14544.36) and add it to both sides. Add '14544.36' to each side of the equation. 241.2r + 14544.36 + r2 = 9014.542675 + 14544.36 Reorder the terms: 14544.36 + 241.2r + r2 = 9014.542675 + 14544.36 Combine like terms: 9014.542675 + 14544.36 = 23558.902675 14544.36 + 241.2r + r2 = 23558.902675 Factor a perfect square on the left side: (r + 120.6)(r + 120.6) = 23558.902675 Calculate the square root of the right side: 153.489096274 Break this problem into two subproblems by setting (r + 120.6) equal to 153.489096274 and -153.489096274.Subproblem 1
r + 120.6 = 153.489096274 Simplifying r + 120.6 = 153.489096274 Reorder the terms: 120.6 + r = 153.489096274 Solving 120.6 + r = 153.489096274 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-120.6' to each side of the equation. 120.6 + -120.6 + r = 153.489096274 + -120.6 Combine like terms: 120.6 + -120.6 = 0.0 0.0 + r = 153.489096274 + -120.6 r = 153.489096274 + -120.6 Combine like terms: 153.489096274 + -120.6 = 32.889096274 r = 32.889096274 Simplifying r = 32.889096274Subproblem 2
r + 120.6 = -153.489096274 Simplifying r + 120.6 = -153.489096274 Reorder the terms: 120.6 + r = -153.489096274 Solving 120.6 + r = -153.489096274 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-120.6' to each side of the equation. 120.6 + -120.6 + r = -153.489096274 + -120.6 Combine like terms: 120.6 + -120.6 = 0.0 0.0 + r = -153.489096274 + -120.6 r = -153.489096274 + -120.6 Combine like terms: -153.489096274 + -120.6 = -274.089096274 r = -274.089096274 Simplifying r = -274.089096274Solution
The solution to the problem is based on the solutions from the subproblems. r = {32.889096274, -274.089096274}
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