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Simplifying 5651.8116 = 6.28r2 + 128.6584r Reorder the terms: 5651.8116 = 128.6584r + 6.28r2 Solving 5651.8116 = 128.6584r + 6.28r2 Solving for variable 'r'. Reorder the terms: 5651.8116 + -128.6584r + -6.28r2 = 128.6584r + -128.6584r + 6.28r2 + -6.28r2 Combine like terms: 128.6584r + -128.6584r = 0.0000 5651.8116 + -128.6584r + -6.28r2 = 0.0000 + 6.28r2 + -6.28r2 5651.8116 + -128.6584r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 5651.8116 + -128.6584r + -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 + 20.48700637r + r2 = 0 Move the constant term to the right: Add '899.97' to each side of the equation. -899.97 + 20.48700637r + 899.97 + r2 = 0 + 899.97 Reorder the terms: -899.97 + 899.97 + 20.48700637r + r2 = 0 + 899.97 Combine like terms: -899.97 + 899.97 = 0.00 0.00 + 20.48700637r + r2 = 0 + 899.97 20.48700637r + r2 = 0 + 899.97 Combine like terms: 0 + 899.97 = 899.97 20.48700637r + r2 = 899.97 The r term is 20.48700637r. Take half its coefficient (10.24350319). Square it (104.9293576) and add it to both sides. Add '104.9293576' to each side of the equation. 20.48700637r + 104.9293576 + r2 = 899.97 + 104.9293576 Reorder the terms: 104.9293576 + 20.48700637r + r2 = 899.97 + 104.9293576 Combine like terms: 899.97 + 104.9293576 = 1004.8993576 104.9293576 + 20.48700637r + r2 = 1004.8993576 Factor a perfect square on the left side: (r + 10.24350319)(r + 10.24350319) = 1004.8993576 Calculate the square root of the right side: 31.700147596 Break this problem into two subproblems by setting (r + 10.24350319) equal to 31.700147596 and -31.700147596.Subproblem 1
r + 10.24350319 = 31.700147596 Simplifying r + 10.24350319 = 31.700147596 Reorder the terms: 10.24350319 + r = 31.700147596 Solving 10.24350319 + r = 31.700147596 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10.24350319' to each side of the equation. 10.24350319 + -10.24350319 + r = 31.700147596 + -10.24350319 Combine like terms: 10.24350319 + -10.24350319 = 0.00000000 0.00000000 + r = 31.700147596 + -10.24350319 r = 31.700147596 + -10.24350319 Combine like terms: 31.700147596 + -10.24350319 = 21.456644406 r = 21.456644406 Simplifying r = 21.456644406Subproblem 2
r + 10.24350319 = -31.700147596 Simplifying r + 10.24350319 = -31.700147596 Reorder the terms: 10.24350319 + r = -31.700147596 Solving 10.24350319 + r = -31.700147596 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10.24350319' to each side of the equation. 10.24350319 + -10.24350319 + r = -31.700147596 + -10.24350319 Combine like terms: 10.24350319 + -10.24350319 = 0.00000000 0.00000000 + r = -31.700147596 + -10.24350319 r = -31.700147596 + -10.24350319 Combine like terms: -31.700147596 + -10.24350319 = -41.943650786 r = -41.943650786 Simplifying r = -41.943650786Solution
The solution to the problem is based on the solutions from the subproblems. r = {21.456644406, -41.943650786}
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