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Simplifying 0 = 6.28r2 + 146.952r + -1175.0508 Reorder the terms: 0 = -1175.0508 + 146.952r + 6.28r2 Solving 0 = -1175.0508 + 146.952r + 6.28r2 Solving for variable 'r'. Combine like terms: 0 + 1175.0508 = 1175.0508 1175.0508 + -146.952r + -6.28r2 = -1175.0508 + 146.952r + 6.28r2 + 1175.0508 + -146.952r + -6.28r2 Reorder the terms: 1175.0508 + -146.952r + -6.28r2 = -1175.0508 + 1175.0508 + 146.952r + -146.952r + 6.28r2 + -6.28r2 Combine like terms: -1175.0508 + 1175.0508 = 0.0000 1175.0508 + -146.952r + -6.28r2 = 0.0000 + 146.952r + -146.952r + 6.28r2 + -6.28r2 1175.0508 + -146.952r + -6.28r2 = 146.952r + -146.952r + 6.28r2 + -6.28r2 Combine like terms: 146.952r + -146.952r = 0.000 1175.0508 + -146.952r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 1175.0508 + -146.952r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 1175.0508 + -146.952r + -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'. -187.11 + 23.4r + r2 = 0 Move the constant term to the right: Add '187.11' to each side of the equation. -187.11 + 23.4r + 187.11 + r2 = 0 + 187.11 Reorder the terms: -187.11 + 187.11 + 23.4r + r2 = 0 + 187.11 Combine like terms: -187.11 + 187.11 = 0.00 0.00 + 23.4r + r2 = 0 + 187.11 23.4r + r2 = 0 + 187.11 Combine like terms: 0 + 187.11 = 187.11 23.4r + r2 = 187.11 The r term is 23.4r. Take half its coefficient (11.7). Square it (136.89) and add it to both sides. Add '136.89' to each side of the equation. 23.4r + 136.89 + r2 = 187.11 + 136.89 Reorder the terms: 136.89 + 23.4r + r2 = 187.11 + 136.89 Combine like terms: 187.11 + 136.89 = 324 136.89 + 23.4r + r2 = 324 Factor a perfect square on the left side: (r + 11.7)(r + 11.7) = 324 Calculate the square root of the right side: 18 Break this problem into two subproblems by setting (r + 11.7) equal to 18 and -18.Subproblem 1
r + 11.7 = 18 Simplifying r + 11.7 = 18 Reorder the terms: 11.7 + r = 18 Solving 11.7 + r = 18 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-11.7' to each side of the equation. 11.7 + -11.7 + r = 18 + -11.7 Combine like terms: 11.7 + -11.7 = 0.0 0.0 + r = 18 + -11.7 r = 18 + -11.7 Combine like terms: 18 + -11.7 = 6.3 r = 6.3 Simplifying r = 6.3Subproblem 2
r + 11.7 = -18 Simplifying r + 11.7 = -18 Reorder the terms: 11.7 + r = -18 Solving 11.7 + r = -18 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-11.7' to each side of the equation. 11.7 + -11.7 + r = -18 + -11.7 Combine like terms: 11.7 + -11.7 = 0.0 0.0 + r = -18 + -11.7 r = -18 + -11.7 Combine like terms: -18 + -11.7 = -29.7 r = -29.7 Simplifying r = -29.7Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.3, -29.7}
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