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Simplifying 0 = 6.28r2 + 1821.2r + -25722.88 Reorder the terms: 0 = -25722.88 + 1821.2r + 6.28r2 Solving 0 = -25722.88 + 1821.2r + 6.28r2 Solving for variable 'r'. Combine like terms: 0 + 25722.88 = 25722.88 25722.88 + -1821.2r + -6.28r2 = -25722.88 + 1821.2r + 6.28r2 + 25722.88 + -1821.2r + -6.28r2 Reorder the terms: 25722.88 + -1821.2r + -6.28r2 = -25722.88 + 25722.88 + 1821.2r + -1821.2r + 6.28r2 + -6.28r2 Combine like terms: -25722.88 + 25722.88 = 0.00 25722.88 + -1821.2r + -6.28r2 = 0.00 + 1821.2r + -1821.2r + 6.28r2 + -6.28r2 25722.88 + -1821.2r + -6.28r2 = 1821.2r + -1821.2r + 6.28r2 + -6.28r2 Combine like terms: 1821.2r + -1821.2r = 0.0 25722.88 + -1821.2r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2 25722.88 + -1821.2r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 25722.88 + -1821.2r + -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'. -4096 + 290r + r2 = 0 Move the constant term to the right: Add '4096' to each side of the equation. -4096 + 290r + 4096 + r2 = 0 + 4096 Reorder the terms: -4096 + 4096 + 290r + r2 = 0 + 4096 Combine like terms: -4096 + 4096 = 0 0 + 290r + r2 = 0 + 4096 290r + r2 = 0 + 4096 Combine like terms: 0 + 4096 = 4096 290r + r2 = 4096 The r term is 290r. Take half its coefficient (145). Square it (21025) and add it to both sides. Add '21025' to each side of the equation. 290r + 21025 + r2 = 4096 + 21025 Reorder the terms: 21025 + 290r + r2 = 4096 + 21025 Combine like terms: 4096 + 21025 = 25121 21025 + 290r + r2 = 25121 Factor a perfect square on the left side: (r + 145)(r + 145) = 25121 Calculate the square root of the right side: 158.496056733 Break this problem into two subproblems by setting (r + 145) equal to 158.496056733 and -158.496056733.Subproblem 1
r + 145 = 158.496056733 Simplifying r + 145 = 158.496056733 Reorder the terms: 145 + r = 158.496056733 Solving 145 + r = 158.496056733 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-145' to each side of the equation. 145 + -145 + r = 158.496056733 + -145 Combine like terms: 145 + -145 = 0 0 + r = 158.496056733 + -145 r = 158.496056733 + -145 Combine like terms: 158.496056733 + -145 = 13.496056733 r = 13.496056733 Simplifying r = 13.496056733Subproblem 2
r + 145 = -158.496056733 Simplifying r + 145 = -158.496056733 Reorder the terms: 145 + r = -158.496056733 Solving 145 + r = -158.496056733 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-145' to each side of the equation. 145 + -145 + r = -158.496056733 + -145 Combine like terms: 145 + -145 = 0 0 + r = -158.496056733 + -145 r = -158.496056733 + -145 Combine like terms: -158.496056733 + -145 = -303.496056733 r = -303.496056733 Simplifying r = -303.496056733Solution
The solution to the problem is based on the solutions from the subproblems. r = {13.496056733, -303.496056733}
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