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Simplifying 285.9912 = 2 * 3.14r2 + 2 * 3.14r * 4 Multiply 2 * 3.14 285.9912 = 6.28r2 + 2 * 3.14r * 4 Reorder the terms for easier multiplication: 285.9912 = 6.28r2 + 2 * 3.14 * 4r Multiply 2 * 3.14 285.9912 = 6.28r2 + 6.28 * 4r Multiply 6.28 * 4 285.9912 = 6.28r2 + 25.12r Reorder the terms: 285.9912 = 25.12r + 6.28r2 Solving 285.9912 = 25.12r + 6.28r2 Solving for variable 'r'. Reorder the terms: 285.9912 + -25.12r + -6.28r2 = 25.12r + -25.12r + 6.28r2 + -6.28r2 Combine like terms: 25.12r + -25.12r = 0.00 285.9912 + -25.12r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 285.9912 + -25.12r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 285.9912 + -25.12r + -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 + 4r + r2 = 0 Move the constant term to the right: Add '45.54' to each side of the equation. -45.54 + 4r + 45.54 + r2 = 0 + 45.54 Reorder the terms: -45.54 + 45.54 + 4r + r2 = 0 + 45.54 Combine like terms: -45.54 + 45.54 = 0.00 0.00 + 4r + r2 = 0 + 45.54 4r + r2 = 0 + 45.54 Combine like terms: 0 + 45.54 = 45.54 4r + r2 = 45.54 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = 45.54 + 4 Reorder the terms: 4 + 4r + r2 = 45.54 + 4 Combine like terms: 45.54 + 4 = 49.54 4 + 4r + r2 = 49.54 Factor a perfect square on the left side: (r + 2)(r + 2) = 49.54 Calculate the square root of the right side: 7.038465742 Break this problem into two subproblems by setting (r + 2) equal to 7.038465742 and -7.038465742.Subproblem 1
r + 2 = 7.038465742 Simplifying r + 2 = 7.038465742 Reorder the terms: 2 + r = 7.038465742 Solving 2 + r = 7.038465742 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 7.038465742 + -2 Combine like terms: 2 + -2 = 0 0 + r = 7.038465742 + -2 r = 7.038465742 + -2 Combine like terms: 7.038465742 + -2 = 5.038465742 r = 5.038465742 Simplifying r = 5.038465742Subproblem 2
r + 2 = -7.038465742 Simplifying r + 2 = -7.038465742 Reorder the terms: 2 + r = -7.038465742 Solving 2 + r = -7.038465742 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -7.038465742 + -2 Combine like terms: 2 + -2 = 0 0 + r = -7.038465742 + -2 r = -7.038465742 + -2 Combine like terms: -7.038465742 + -2 = -9.038465742 r = -9.038465742 Simplifying r = -9.038465742Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.038465742, -9.038465742}
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