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Simplifying 200.96 = 2 * 3.14r2 + 2 * 3.14r * 4 Multiply 2 * 3.14 200.96 = 6.28r2 + 2 * 3.14r * 4 Reorder the terms for easier multiplication: 200.96 = 6.28r2 + 2 * 3.14 * 4r Multiply 2 * 3.14 200.96 = 6.28r2 + 6.28 * 4r Multiply 6.28 * 4 200.96 = 6.28r2 + 25.12r Reorder the terms: 200.96 = 25.12r + 6.28r2 Solving 200.96 = 25.12r + 6.28r2 Solving for variable 'r'. Reorder the terms: 200.96 + -25.12r + -6.28r2 = 25.12r + -25.12r + 6.28r2 + -6.28r2 Combine like terms: 25.12r + -25.12r = 0.00 200.96 + -25.12r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 200.96 + -25.12r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 200.96 + -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'. -32 + 4r + r2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 4r + 32 + r2 = 0 + 32 Reorder the terms: -32 + 32 + 4r + r2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 4r + r2 = 0 + 32 4r + r2 = 0 + 32 Combine like terms: 0 + 32 = 32 4r + r2 = 32 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 = 32 + 4 Reorder the terms: 4 + 4r + r2 = 32 + 4 Combine like terms: 32 + 4 = 36 4 + 4r + r2 = 36 Factor a perfect square on the left side: (r + 2)(r + 2) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (r + 2) equal to 6 and -6.Subproblem 1
r + 2 = 6 Simplifying r + 2 = 6 Reorder the terms: 2 + r = 6 Solving 2 + r = 6 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 = 6 + -2 Combine like terms: 2 + -2 = 0 0 + r = 6 + -2 r = 6 + -2 Combine like terms: 6 + -2 = 4 r = 4 Simplifying r = 4Subproblem 2
r + 2 = -6 Simplifying r + 2 = -6 Reorder the terms: 2 + r = -6 Solving 2 + r = -6 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 = -6 + -2 Combine like terms: 2 + -2 = 0 0 + r = -6 + -2 r = -6 + -2 Combine like terms: -6 + -2 = -8 r = -8 Simplifying r = -8Solution
The solution to the problem is based on the solutions from the subproblems. r = {4, -8}
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