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Simplifying 1270.444 = 2 * 3.14r2 + 2 * 3.14r * 17.4 Multiply 2 * 3.14 1270.444 = 6.28r2 + 2 * 3.14r * 17.4 Reorder the terms for easier multiplication: 1270.444 = 6.28r2 + 2 * 3.14 * 17.4r Multiply 2 * 3.14 1270.444 = 6.28r2 + 6.28 * 17.4r Multiply 6.28 * 17.4 1270.444 = 6.28r2 + 109.272r Reorder the terms: 1270.444 = 109.272r + 6.28r2 Solving 1270.444 = 109.272r + 6.28r2 Solving for variable 'r'. Reorder the terms: 1270.444 + -109.272r + -6.28r2 = 109.272r + -109.272r + 6.28r2 + -6.28r2 Combine like terms: 109.272r + -109.272r = 0.000 1270.444 + -109.272r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 1270.444 + -109.272r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 1270.444 + -109.272r + -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'. -202.3 + 17.4r + r2 = 0 Move the constant term to the right: Add '202.3' to each side of the equation. -202.3 + 17.4r + 202.3 + r2 = 0 + 202.3 Reorder the terms: -202.3 + 202.3 + 17.4r + r2 = 0 + 202.3 Combine like terms: -202.3 + 202.3 = 0.0 0.0 + 17.4r + r2 = 0 + 202.3 17.4r + r2 = 0 + 202.3 Combine like terms: 0 + 202.3 = 202.3 17.4r + r2 = 202.3 The r term is 17.4r. Take half its coefficient (8.7). Square it (75.69) and add it to both sides. Add '75.69' to each side of the equation. 17.4r + 75.69 + r2 = 202.3 + 75.69 Reorder the terms: 75.69 + 17.4r + r2 = 202.3 + 75.69 Combine like terms: 202.3 + 75.69 = 277.99 75.69 + 17.4r + r2 = 277.99 Factor a perfect square on the left side: (r + 8.7)(r + 8.7) = 277.99 Calculate the square root of the right side: 16.673032118 Break this problem into two subproblems by setting (r + 8.7) equal to 16.673032118 and -16.673032118.Subproblem 1
r + 8.7 = 16.673032118 Simplifying r + 8.7 = 16.673032118 Reorder the terms: 8.7 + r = 16.673032118 Solving 8.7 + r = 16.673032118 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.7' to each side of the equation. 8.7 + -8.7 + r = 16.673032118 + -8.7 Combine like terms: 8.7 + -8.7 = 0.0 0.0 + r = 16.673032118 + -8.7 r = 16.673032118 + -8.7 Combine like terms: 16.673032118 + -8.7 = 7.973032118 r = 7.973032118 Simplifying r = 7.973032118Subproblem 2
r + 8.7 = -16.673032118 Simplifying r + 8.7 = -16.673032118 Reorder the terms: 8.7 + r = -16.673032118 Solving 8.7 + r = -16.673032118 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.7' to each side of the equation. 8.7 + -8.7 + r = -16.673032118 + -8.7 Combine like terms: 8.7 + -8.7 = 0.0 0.0 + r = -16.673032118 + -8.7 r = -16.673032118 + -8.7 Combine like terms: -16.673032118 + -8.7 = -25.373032118 r = -25.373032118 Simplifying r = -25.373032118Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.973032118, -25.373032118}
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