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Simplifying 0 = 6.28r2 + 229.22r + -3318.1008 Reorder the terms: 0 = -3318.1008 + 229.22r + 6.28r2 Solving 0 = -3318.1008 + 229.22r + 6.28r2 Solving for variable 'r'. Combine like terms: 0 + 3318.1008 = 3318.1008 3318.1008 + -229.22r + -6.28r2 = -3318.1008 + 229.22r + 6.28r2 + 3318.1008 + -229.22r + -6.28r2 Reorder the terms: 3318.1008 + -229.22r + -6.28r2 = -3318.1008 + 3318.1008 + 229.22r + -229.22r + 6.28r2 + -6.28r2 Combine like terms: -3318.1008 + 3318.1008 = 0.0000 3318.1008 + -229.22r + -6.28r2 = 0.0000 + 229.22r + -229.22r + 6.28r2 + -6.28r2 3318.1008 + -229.22r + -6.28r2 = 229.22r + -229.22r + 6.28r2 + -6.28r2 Combine like terms: 229.22r + -229.22r = 0.00 3318.1008 + -229.22r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 3318.1008 + -229.22r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 3318.1008 + -229.22r + -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'. -528.36 + 36.5r + r2 = 0 Move the constant term to the right: Add '528.36' to each side of the equation. -528.36 + 36.5r + 528.36 + r2 = 0 + 528.36 Reorder the terms: -528.36 + 528.36 + 36.5r + r2 = 0 + 528.36 Combine like terms: -528.36 + 528.36 = 0.00 0.00 + 36.5r + r2 = 0 + 528.36 36.5r + r2 = 0 + 528.36 Combine like terms: 0 + 528.36 = 528.36 36.5r + r2 = 528.36 The r term is 36.5r. Take half its coefficient (18.25). Square it (333.0625) and add it to both sides. Add '333.0625' to each side of the equation. 36.5r + 333.0625 + r2 = 528.36 + 333.0625 Reorder the terms: 333.0625 + 36.5r + r2 = 528.36 + 333.0625 Combine like terms: 528.36 + 333.0625 = 861.4225 333.0625 + 36.5r + r2 = 861.4225 Factor a perfect square on the left side: (r + 18.25)(r + 18.25) = 861.4225 Calculate the square root of the right side: 29.35 Break this problem into two subproblems by setting (r + 18.25) equal to 29.35 and -29.35.Subproblem 1
r + 18.25 = 29.35 Simplifying r + 18.25 = 29.35 Reorder the terms: 18.25 + r = 29.35 Solving 18.25 + r = 29.35 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-18.25' to each side of the equation. 18.25 + -18.25 + r = 29.35 + -18.25 Combine like terms: 18.25 + -18.25 = 0.00 0.00 + r = 29.35 + -18.25 r = 29.35 + -18.25 Combine like terms: 29.35 + -18.25 = 11.1 r = 11.1 Simplifying r = 11.1Subproblem 2
r + 18.25 = -29.35 Simplifying r + 18.25 = -29.35 Reorder the terms: 18.25 + r = -29.35 Solving 18.25 + r = -29.35 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-18.25' to each side of the equation. 18.25 + -18.25 + r = -29.35 + -18.25 Combine like terms: 18.25 + -18.25 = 0.00 0.00 + r = -29.35 + -18.25 r = -29.35 + -18.25 Combine like terms: -29.35 + -18.25 = -47.6 r = -47.6 Simplifying r = -47.6Solution
The solution to the problem is based on the solutions from the subproblems. r = {11.1, -47.6}
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