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Simplifying 621.72 = 6.28r2 + 112.944r Reorder the terms: 621.72 = 112.944r + 6.28r2 Solving 621.72 = 112.944r + 6.28r2 Solving for variable 'r'. Reorder the terms: 621.72 + -112.944r + -6.28r2 = 112.944r + -112.944r + 6.28r2 + -6.28r2 Combine like terms: 112.944r + -112.944r = 0.000 621.72 + -112.944r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 621.72 + -112.944r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 621.72 + -112.944r + -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'. -99 + 17.98471338r + r2 = 0 Move the constant term to the right: Add '99' to each side of the equation. -99 + 17.98471338r + 99 + r2 = 0 + 99 Reorder the terms: -99 + 99 + 17.98471338r + r2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 17.98471338r + r2 = 0 + 99 17.98471338r + r2 = 0 + 99 Combine like terms: 0 + 99 = 99 17.98471338r + r2 = 99 The r term is 17.98471338r. Take half its coefficient (8.99235669). Square it (80.86247884) and add it to both sides. Add '80.86247884' to each side of the equation. 17.98471338r + 80.86247884 + r2 = 99 + 80.86247884 Reorder the terms: 80.86247884 + 17.98471338r + r2 = 99 + 80.86247884 Combine like terms: 99 + 80.86247884 = 179.86247884 80.86247884 + 17.98471338r + r2 = 179.86247884 Factor a perfect square on the left side: (r + 8.99235669)(r + 8.99235669) = 179.86247884 Calculate the square root of the right side: 13.411281775 Break this problem into two subproblems by setting (r + 8.99235669) equal to 13.411281775 and -13.411281775.Subproblem 1
r + 8.99235669 = 13.411281775 Simplifying r + 8.99235669 = 13.411281775 Reorder the terms: 8.99235669 + r = 13.411281775 Solving 8.99235669 + r = 13.411281775 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.99235669' to each side of the equation. 8.99235669 + -8.99235669 + r = 13.411281775 + -8.99235669 Combine like terms: 8.99235669 + -8.99235669 = 0.00000000 0.00000000 + r = 13.411281775 + -8.99235669 r = 13.411281775 + -8.99235669 Combine like terms: 13.411281775 + -8.99235669 = 4.418925085 r = 4.418925085 Simplifying r = 4.418925085Subproblem 2
r + 8.99235669 = -13.411281775 Simplifying r + 8.99235669 = -13.411281775 Reorder the terms: 8.99235669 + r = -13.411281775 Solving 8.99235669 + r = -13.411281775 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.99235669' to each side of the equation. 8.99235669 + -8.99235669 + r = -13.411281775 + -8.99235669 Combine like terms: 8.99235669 + -8.99235669 = 0.00000000 0.00000000 + r = -13.411281775 + -8.99235669 r = -13.411281775 + -8.99235669 Combine like terms: -13.411281775 + -8.99235669 = -22.403638465 r = -22.403638465 Simplifying r = -22.403638465Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.418925085, -22.403638465}
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