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Simplifying 10889.52 = 6.28r2 + 533.8r Reorder the terms: 10889.52 = 533.8r + 6.28r2 Solving 10889.52 = 533.8r + 6.28r2 Solving for variable 'r'. Reorder the terms: 10889.52 + -533.8r + -6.28r2 = 533.8r + -533.8r + 6.28r2 + -6.28r2 Combine like terms: 533.8r + -533.8r = 0.0 10889.52 + -533.8r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2 10889.52 + -533.8r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 10889.52 + -533.8r + -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'. -1734 + 85r + r2 = 0 Move the constant term to the right: Add '1734' to each side of the equation. -1734 + 85r + 1734 + r2 = 0 + 1734 Reorder the terms: -1734 + 1734 + 85r + r2 = 0 + 1734 Combine like terms: -1734 + 1734 = 0 0 + 85r + r2 = 0 + 1734 85r + r2 = 0 + 1734 Combine like terms: 0 + 1734 = 1734 85r + r2 = 1734 The r term is 85r. Take half its coefficient (42.5). Square it (1806.25) and add it to both sides. Add '1806.25' to each side of the equation. 85r + 1806.25 + r2 = 1734 + 1806.25 Reorder the terms: 1806.25 + 85r + r2 = 1734 + 1806.25 Combine like terms: 1734 + 1806.25 = 3540.25 1806.25 + 85r + r2 = 3540.25 Factor a perfect square on the left side: (r + 42.5)(r + 42.5) = 3540.25 Calculate the square root of the right side: 59.5 Break this problem into two subproblems by setting (r + 42.5) equal to 59.5 and -59.5.Subproblem 1
r + 42.5 = 59.5 Simplifying r + 42.5 = 59.5 Reorder the terms: 42.5 + r = 59.5 Solving 42.5 + r = 59.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-42.5' to each side of the equation. 42.5 + -42.5 + r = 59.5 + -42.5 Combine like terms: 42.5 + -42.5 = 0.0 0.0 + r = 59.5 + -42.5 r = 59.5 + -42.5 Combine like terms: 59.5 + -42.5 = 17 r = 17 Simplifying r = 17Subproblem 2
r + 42.5 = -59.5 Simplifying r + 42.5 = -59.5 Reorder the terms: 42.5 + r = -59.5 Solving 42.5 + r = -59.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-42.5' to each side of the equation. 42.5 + -42.5 + r = -59.5 + -42.5 Combine like terms: 42.5 + -42.5 = 0.0 0.0 + r = -59.5 + -42.5 r = -59.5 + -42.5 Combine like terms: -59.5 + -42.5 = -102 r = -102 Simplifying r = -102Solution
The solution to the problem is based on the solutions from the subproblems. r = {17, -102}
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