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Simplifying 3000 = 3.14 * 100r + 3.14r2 Multiply 3.14 * 100 3000 = 314r + 3.14r2 Solving 3000 = 314r + 3.14r2 Solving for variable 'r'. Reorder the terms: 3000 + -314r + -3.14r2 = 314r + -314r + 3.14r2 + -3.14r2 Combine like terms: 314r + -314r = 0 3000 + -314r + -3.14r2 = 0 + 3.14r2 + -3.14r2 3000 + -314r + -3.14r2 = 3.14r2 + -3.14r2 Combine like terms: 3.14r2 + -3.14r2 = 0.00 3000 + -314r + -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'. -955.4140127 + 100r + r2 = 0 Move the constant term to the right: Add '955.4140127' to each side of the equation. -955.4140127 + 100r + 955.4140127 + r2 = 0 + 955.4140127 Reorder the terms: -955.4140127 + 955.4140127 + 100r + r2 = 0 + 955.4140127 Combine like terms: -955.4140127 + 955.4140127 = 0.0000000 0.0000000 + 100r + r2 = 0 + 955.4140127 100r + r2 = 0 + 955.4140127 Combine like terms: 0 + 955.4140127 = 955.4140127 100r + r2 = 955.4140127 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 = 955.4140127 + 2500 Reorder the terms: 2500 + 100r + r2 = 955.4140127 + 2500 Combine like terms: 955.4140127 + 2500 = 3455.4140127 2500 + 100r + r2 = 3455.4140127 Factor a perfect square on the left side: (r + 50)(r + 50) = 3455.4140127 Calculate the square root of the right side: 58.782769692 Break this problem into two subproblems by setting (r + 50) equal to 58.782769692 and -58.782769692.Subproblem 1
r + 50 = 58.782769692 Simplifying r + 50 = 58.782769692 Reorder the terms: 50 + r = 58.782769692 Solving 50 + r = 58.782769692 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 = 58.782769692 + -50 Combine like terms: 50 + -50 = 0 0 + r = 58.782769692 + -50 r = 58.782769692 + -50 Combine like terms: 58.782769692 + -50 = 8.782769692 r = 8.782769692 Simplifying r = 8.782769692Subproblem 2
r + 50 = -58.782769692 Simplifying r + 50 = -58.782769692 Reorder the terms: 50 + r = -58.782769692 Solving 50 + r = -58.782769692 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 = -58.782769692 + -50 Combine like terms: 50 + -50 = 0 0 + r = -58.782769692 + -50 r = -58.782769692 + -50 Combine like terms: -58.782769692 + -50 = -108.782769692 r = -108.782769692 Simplifying r = -108.782769692Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.782769692, -108.782769692}
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