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Simplifying 550 = 2 * 3.14 * 25r + 3.14r2 Multiply 2 * 3.14 550 = 6.28 * 25r + 3.14r2 Multiply 6.28 * 25 550 = 157r + 3.14r2 Solving 550 = 157r + 3.14r2 Solving for variable 'r'. Reorder the terms: 550 + -157r + -3.14r2 = 157r + -157r + 3.14r2 + -3.14r2 Combine like terms: 157r + -157r = 0 550 + -157r + -3.14r2 = 0 + 3.14r2 + -3.14r2 550 + -157r + -3.14r2 = 3.14r2 + -3.14r2 Combine like terms: 3.14r2 + -3.14r2 = 0.00 550 + -157r + -3.14r2 = 0.00 Begin completing the square. Divide all terms by -3.14 the coefficient of the squared term: Divide each side by '-3.14'. -175.1592357 + 50r + r2 = 0 Move the constant term to the right: Add '175.1592357' to each side of the equation. -175.1592357 + 50r + 175.1592357 + r2 = 0 + 175.1592357 Reorder the terms: -175.1592357 + 175.1592357 + 50r + r2 = 0 + 175.1592357 Combine like terms: -175.1592357 + 175.1592357 = 0.0000000 0.0000000 + 50r + r2 = 0 + 175.1592357 50r + r2 = 0 + 175.1592357 Combine like terms: 0 + 175.1592357 = 175.1592357 50r + r2 = 175.1592357 The r term is 50r. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50r + 625 + r2 = 175.1592357 + 625 Reorder the terms: 625 + 50r + r2 = 175.1592357 + 625 Combine like terms: 175.1592357 + 625 = 800.1592357 625 + 50r + r2 = 800.1592357 Factor a perfect square on the left side: (r + 25)(r + 25) = 800.1592357 Calculate the square root of the right side: 28.287086023 Break this problem into two subproblems by setting (r + 25) equal to 28.287086023 and -28.287086023.Subproblem 1
r + 25 = 28.287086023 Simplifying r + 25 = 28.287086023 Reorder the terms: 25 + r = 28.287086023 Solving 25 + r = 28.287086023 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + r = 28.287086023 + -25 Combine like terms: 25 + -25 = 0 0 + r = 28.287086023 + -25 r = 28.287086023 + -25 Combine like terms: 28.287086023 + -25 = 3.287086023 r = 3.287086023 Simplifying r = 3.287086023Subproblem 2
r + 25 = -28.287086023 Simplifying r + 25 = -28.287086023 Reorder the terms: 25 + r = -28.287086023 Solving 25 + r = -28.287086023 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + r = -28.287086023 + -25 Combine like terms: 25 + -25 = 0 0 + r = -28.287086023 + -25 r = -28.287086023 + -25 Combine like terms: -28.287086023 + -25 = -53.287086023 r = -53.287086023 Simplifying r = -53.287086023Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.287086023, -53.287086023}
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