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Simplifying 285.9912 = 6.28r2 + 33.125r Reorder the terms: 285.9912 = 33.125r + 6.28r2 Solving 285.9912 = 33.125r + 6.28r2 Solving for variable 'r'. Reorder the terms: 285.9912 + -33.125r + -6.28r2 = 33.125r + -33.125r + 6.28r2 + -6.28r2 Combine like terms: 33.125r + -33.125r = 0.000 285.9912 + -33.125r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 285.9912 + -33.125r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 285.9912 + -33.125r + -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'. -45.54 + 5.274681529r + r2 = 0 Move the constant term to the right: Add '45.54' to each side of the equation. -45.54 + 5.274681529r + 45.54 + r2 = 0 + 45.54 Reorder the terms: -45.54 + 45.54 + 5.274681529r + r2 = 0 + 45.54 Combine like terms: -45.54 + 45.54 = 0.00 0.00 + 5.274681529r + r2 = 0 + 45.54 5.274681529r + r2 = 0 + 45.54 Combine like terms: 0 + 45.54 = 45.54 5.274681529r + r2 = 45.54 The r term is 5.274681529r. Take half its coefficient (2.637340765). Square it (6.955566311) and add it to both sides. Add '6.955566311' to each side of the equation. 5.274681529r + 6.955566311 + r2 = 45.54 + 6.955566311 Reorder the terms: 6.955566311 + 5.274681529r + r2 = 45.54 + 6.955566311 Combine like terms: 45.54 + 6.955566311 = 52.495566311 6.955566311 + 5.274681529r + r2 = 52.495566311 Factor a perfect square on the left side: (r + 2.637340765)(r + 2.637340765) = 52.495566311 Calculate the square root of the right side: 7.245382413 Break this problem into two subproblems by setting (r + 2.637340765) equal to 7.245382413 and -7.245382413.Subproblem 1
r + 2.637340765 = 7.245382413 Simplifying r + 2.637340765 = 7.245382413 Reorder the terms: 2.637340765 + r = 7.245382413 Solving 2.637340765 + r = 7.245382413 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.637340765' to each side of the equation. 2.637340765 + -2.637340765 + r = 7.245382413 + -2.637340765 Combine like terms: 2.637340765 + -2.637340765 = 0.000000000 0.000000000 + r = 7.245382413 + -2.637340765 r = 7.245382413 + -2.637340765 Combine like terms: 7.245382413 + -2.637340765 = 4.608041648 r = 4.608041648 Simplifying r = 4.608041648Subproblem 2
r + 2.637340765 = -7.245382413 Simplifying r + 2.637340765 = -7.245382413 Reorder the terms: 2.637340765 + r = -7.245382413 Solving 2.637340765 + r = -7.245382413 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.637340765' to each side of the equation. 2.637340765 + -2.637340765 + r = -7.245382413 + -2.637340765 Combine like terms: 2.637340765 + -2.637340765 = 0.000000000 0.000000000 + r = -7.245382413 + -2.637340765 r = -7.245382413 + -2.637340765 Combine like terms: -7.245382413 + -2.637340765 = -9.882723178 r = -9.882723178 Simplifying r = -9.882723178Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.608041648, -9.882723178}
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