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Simplifying 756.74 = 6.28r2 + 119.948r Reorder the terms: 756.74 = 119.948r + 6.28r2 Solving 756.74 = 119.948r + 6.28r2 Solving for variable 'r'. Reorder the terms: 756.74 + -119.948r + -6.28r2 = 119.948r + -119.948r + 6.28r2 + -6.28r2 Combine like terms: 119.948r + -119.948r = 0.000 756.74 + -119.948r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 756.74 + -119.948r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 756.74 + -119.948r + -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'. -120.5 + 19.1r + r2 = 0 Move the constant term to the right: Add '120.5' to each side of the equation. -120.5 + 19.1r + 120.5 + r2 = 0 + 120.5 Reorder the terms: -120.5 + 120.5 + 19.1r + r2 = 0 + 120.5 Combine like terms: -120.5 + 120.5 = 0.0 0.0 + 19.1r + r2 = 0 + 120.5 19.1r + r2 = 0 + 120.5 Combine like terms: 0 + 120.5 = 120.5 19.1r + r2 = 120.5 The r term is 19.1r. Take half its coefficient (9.55). Square it (91.2025) and add it to both sides. Add '91.2025' to each side of the equation. 19.1r + 91.2025 + r2 = 120.5 + 91.2025 Reorder the terms: 91.2025 + 19.1r + r2 = 120.5 + 91.2025 Combine like terms: 120.5 + 91.2025 = 211.7025 91.2025 + 19.1r + r2 = 211.7025 Factor a perfect square on the left side: (r + 9.55)(r + 9.55) = 211.7025 Calculate the square root of the right side: 14.55 Break this problem into two subproblems by setting (r + 9.55) equal to 14.55 and -14.55.Subproblem 1
r + 9.55 = 14.55 Simplifying r + 9.55 = 14.55 Reorder the terms: 9.55 + r = 14.55 Solving 9.55 + r = 14.55 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9.55' to each side of the equation. 9.55 + -9.55 + r = 14.55 + -9.55 Combine like terms: 9.55 + -9.55 = 0.00 0.00 + r = 14.55 + -9.55 r = 14.55 + -9.55 Combine like terms: 14.55 + -9.55 = 5 r = 5 Simplifying r = 5Subproblem 2
r + 9.55 = -14.55 Simplifying r + 9.55 = -14.55 Reorder the terms: 9.55 + r = -14.55 Solving 9.55 + r = -14.55 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9.55' to each side of the equation. 9.55 + -9.55 + r = -14.55 + -9.55 Combine like terms: 9.55 + -9.55 = 0.00 0.00 + r = -14.55 + -9.55 r = -14.55 + -9.55 Combine like terms: -14.55 + -9.55 = -24.1 r = -24.1 Simplifying r = -24.1Solution
The solution to the problem is based on the solutions from the subproblems. r = {5, -24.1}
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