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Simplifying 965.36 = 2 * 3.14r(r) + 2 * 3.14r * 9.9 Multiply 2 * 3.14 965.36 = 6.28r * r + 2 * 3.14r * 9.9 Multiply r * r 965.36 = 6.28r2 + 2 * 3.14r * 9.9 Reorder the terms for easier multiplication: 965.36 = 6.28r2 + 2 * 3.14 * 9.9r Multiply 2 * 3.14 965.36 = 6.28r2 + 6.28 * 9.9r Multiply 6.28 * 9.9 965.36 = 6.28r2 + 62.172r Reorder the terms: 965.36 = 62.172r + 6.28r2 Solving 965.36 = 62.172r + 6.28r2 Solving for variable 'r'. Reorder the terms: 965.36 + -62.172r + -6.28r2 = 62.172r + -62.172r + 6.28r2 + -6.28r2 Combine like terms: 62.172r + -62.172r = 0.000 965.36 + -62.172r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 965.36 + -62.172r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 965.36 + -62.172r + -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'. -153.7197452 + 9.9r + r2 = 0 Move the constant term to the right: Add '153.7197452' to each side of the equation. -153.7197452 + 9.9r + 153.7197452 + r2 = 0 + 153.7197452 Reorder the terms: -153.7197452 + 153.7197452 + 9.9r + r2 = 0 + 153.7197452 Combine like terms: -153.7197452 + 153.7197452 = 0.0000000 0.0000000 + 9.9r + r2 = 0 + 153.7197452 9.9r + r2 = 0 + 153.7197452 Combine like terms: 0 + 153.7197452 = 153.7197452 9.9r + r2 = 153.7197452 The r term is 9.9r. Take half its coefficient (4.95). Square it (24.5025) and add it to both sides. Add '24.5025' to each side of the equation. 9.9r + 24.5025 + r2 = 153.7197452 + 24.5025 Reorder the terms: 24.5025 + 9.9r + r2 = 153.7197452 + 24.5025 Combine like terms: 153.7197452 + 24.5025 = 178.2222452 24.5025 + 9.9r + r2 = 178.2222452 Factor a perfect square on the left side: (r + 4.95)(r + 4.95) = 178.2222452 Calculate the square root of the right side: 13.349990457 Break this problem into two subproblems by setting (r + 4.95) equal to 13.349990457 and -13.349990457.Subproblem 1
r + 4.95 = 13.349990457 Simplifying r + 4.95 = 13.349990457 Reorder the terms: 4.95 + r = 13.349990457 Solving 4.95 + r = 13.349990457 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.95' to each side of the equation. 4.95 + -4.95 + r = 13.349990457 + -4.95 Combine like terms: 4.95 + -4.95 = 0.00 0.00 + r = 13.349990457 + -4.95 r = 13.349990457 + -4.95 Combine like terms: 13.349990457 + -4.95 = 8.399990457 r = 8.399990457 Simplifying r = 8.399990457Subproblem 2
r + 4.95 = -13.349990457 Simplifying r + 4.95 = -13.349990457 Reorder the terms: 4.95 + r = -13.349990457 Solving 4.95 + r = -13.349990457 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.95' to each side of the equation. 4.95 + -4.95 + r = -13.349990457 + -4.95 Combine like terms: 4.95 + -4.95 = 0.00 0.00 + r = -13.349990457 + -4.95 r = -13.349990457 + -4.95 Combine like terms: -13.349990457 + -4.95 = -18.299990457 r = -18.299990457 Simplifying r = -18.299990457Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.399990457, -18.299990457}
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