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Simplifying 314.1592654r + 3.141592654r2 = 3000 Solving 314.1592654r + 3.141592654r2 = 3000 Solving for variable 'r'. Reorder the terms: -3000 + 314.1592654r + 3.141592654r2 = 3000 + -3000 Combine like terms: 3000 + -3000 = 0 -3000 + 314.1592654r + 3.141592654r2 = 0 Begin completing the square. Divide all terms by 3.141592654 the coefficient of the squared term: Divide each side by '3.141592654'. -954.9296584 + 100r + r2 = 0 Move the constant term to the right: Add '954.9296584' to each side of the equation. -954.9296584 + 100r + 954.9296584 + r2 = 0 + 954.9296584 Reorder the terms: -954.9296584 + 954.9296584 + 100r + r2 = 0 + 954.9296584 Combine like terms: -954.9296584 + 954.9296584 = 0.0000000 0.0000000 + 100r + r2 = 0 + 954.9296584 100r + r2 = 0 + 954.9296584 Combine like terms: 0 + 954.9296584 = 954.9296584 100r + r2 = 954.9296584 The r term is 100r. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100r + 2500 + r2 = 954.9296584 + 2500 Reorder the terms: 2500 + 100r + r2 = 954.9296584 + 2500 Combine like terms: 954.9296584 + 2500 = 3454.9296584 2500 + 100r + r2 = 3454.9296584 Factor a perfect square on the left side: (r + 50)(r + 50) = 3454.9296584 Calculate the square root of the right side: 58.778649682 Break this problem into two subproblems by setting (r + 50) equal to 58.778649682 and -58.778649682.Subproblem 1
r + 50 = 58.778649682 Simplifying r + 50 = 58.778649682 Reorder the terms: 50 + r = 58.778649682 Solving 50 + r = 58.778649682 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + r = 58.778649682 + -50 Combine like terms: 50 + -50 = 0 0 + r = 58.778649682 + -50 r = 58.778649682 + -50 Combine like terms: 58.778649682 + -50 = 8.778649682 r = 8.778649682 Simplifying r = 8.778649682Subproblem 2
r + 50 = -58.778649682 Simplifying r + 50 = -58.778649682 Reorder the terms: 50 + r = -58.778649682 Solving 50 + r = -58.778649682 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + r = -58.778649682 + -50 Combine like terms: 50 + -50 = 0 0 + r = -58.778649682 + -50 r = -58.778649682 + -50 Combine like terms: -58.778649682 + -50 = -108.778649682 r = -108.778649682 Simplifying r = -108.778649682Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.778649682, -108.778649682}
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