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Simplifying 1133.9168 = 6.28r2 + 147.58r Reorder the terms: 1133.9168 = 147.58r + 6.28r2 Solving 1133.9168 = 147.58r + 6.28r2 Solving for variable 'r'. Reorder the terms: 1133.9168 + -147.58r + -6.28r2 = 147.58r + -147.58r + 6.28r2 + -6.28r2 Combine like terms: 147.58r + -147.58r = 0.00 1133.9168 + -147.58r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 1133.9168 + -147.58r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 1133.9168 + -147.58r + -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'. -180.56 + 23.5r + r2 = 0 Move the constant term to the right: Add '180.56' to each side of the equation. -180.56 + 23.5r + 180.56 + r2 = 0 + 180.56 Reorder the terms: -180.56 + 180.56 + 23.5r + r2 = 0 + 180.56 Combine like terms: -180.56 + 180.56 = 0.00 0.00 + 23.5r + r2 = 0 + 180.56 23.5r + r2 = 0 + 180.56 Combine like terms: 0 + 180.56 = 180.56 23.5r + r2 = 180.56 The r term is 23.5r. Take half its coefficient (11.75). Square it (138.0625) and add it to both sides. Add '138.0625' to each side of the equation. 23.5r + 138.0625 + r2 = 180.56 + 138.0625 Reorder the terms: 138.0625 + 23.5r + r2 = 180.56 + 138.0625 Combine like terms: 180.56 + 138.0625 = 318.6225 138.0625 + 23.5r + r2 = 318.6225 Factor a perfect square on the left side: (r + 11.75)(r + 11.75) = 318.6225 Calculate the square root of the right side: 17.85 Break this problem into two subproblems by setting (r + 11.75) equal to 17.85 and -17.85.Subproblem 1
r + 11.75 = 17.85 Simplifying r + 11.75 = 17.85 Reorder the terms: 11.75 + r = 17.85 Solving 11.75 + r = 17.85 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-11.75' to each side of the equation. 11.75 + -11.75 + r = 17.85 + -11.75 Combine like terms: 11.75 + -11.75 = 0.00 0.00 + r = 17.85 + -11.75 r = 17.85 + -11.75 Combine like terms: 17.85 + -11.75 = 6.1 r = 6.1 Simplifying r = 6.1Subproblem 2
r + 11.75 = -17.85 Simplifying r + 11.75 = -17.85 Reorder the terms: 11.75 + r = -17.85 Solving 11.75 + r = -17.85 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-11.75' to each side of the equation. 11.75 + -11.75 + r = -17.85 + -11.75 Combine like terms: 11.75 + -11.75 = 0.00 0.00 + r = -17.85 + -11.75 r = -17.85 + -11.75 Combine like terms: -17.85 + -11.75 = -29.6 r = -29.6 Simplifying r = -29.6Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.1, -29.6}
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