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Simplifying 3523 = 2 * 3.14r * 40 + 2 * 3.14r2 Reorder the terms for easier multiplication: 3523 = 2 * 3.14 * 40r + 2 * 3.14r2 Multiply 2 * 3.14 3523 = 6.28 * 40r + 2 * 3.14r2 Multiply 6.28 * 40 3523 = 251.2r + 2 * 3.14r2 Multiply 2 * 3.14 3523 = 251.2r + 6.28r2 Solving 3523 = 251.2r + 6.28r2 Solving for variable 'r'. Reorder the terms: 3523 + -251.2r + -6.28r2 = 251.2r + -251.2r + 6.28r2 + -6.28r2 Combine like terms: 251.2r + -251.2r = 0.0 3523 + -251.2r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2 3523 + -251.2r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 3523 + -251.2r + -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'. -560.9872611 + 40r + r2 = 0 Move the constant term to the right: Add '560.9872611' to each side of the equation. -560.9872611 + 40r + 560.9872611 + r2 = 0 + 560.9872611 Reorder the terms: -560.9872611 + 560.9872611 + 40r + r2 = 0 + 560.9872611 Combine like terms: -560.9872611 + 560.9872611 = 0.0000000 0.0000000 + 40r + r2 = 0 + 560.9872611 40r + r2 = 0 + 560.9872611 Combine like terms: 0 + 560.9872611 = 560.9872611 40r + r2 = 560.9872611 The r term is 40r. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40r + 400 + r2 = 560.9872611 + 400 Reorder the terms: 400 + 40r + r2 = 560.9872611 + 400 Combine like terms: 560.9872611 + 400 = 960.9872611 400 + 40r + r2 = 960.9872611 Factor a perfect square on the left side: (r + 20)(r + 20) = 960.9872611 Calculate the square root of the right side: 30.999794533 Break this problem into two subproblems by setting (r + 20) equal to 30.999794533 and -30.999794533.Subproblem 1
r + 20 = 30.999794533 Simplifying r + 20 = 30.999794533 Reorder the terms: 20 + r = 30.999794533 Solving 20 + r = 30.999794533 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + r = 30.999794533 + -20 Combine like terms: 20 + -20 = 0 0 + r = 30.999794533 + -20 r = 30.999794533 + -20 Combine like terms: 30.999794533 + -20 = 10.999794533 r = 10.999794533 Simplifying r = 10.999794533Subproblem 2
r + 20 = -30.999794533 Simplifying r + 20 = -30.999794533 Reorder the terms: 20 + r = -30.999794533 Solving 20 + r = -30.999794533 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + r = -30.999794533 + -20 Combine like terms: 20 + -20 = 0 0 + r = -30.999794533 + -20 r = -30.999794533 + -20 Combine like terms: -30.999794533 + -20 = -50.999794533 r = -50.999794533 Simplifying r = -50.999794533Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.999794533, -50.999794533}
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