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Simplifying 94.9536 = 2 * 3.14r2 + 2 * 3.14r * 1.8 Multiply 2 * 3.14 94.9536 = 6.28r2 + 2 * 3.14r * 1.8 Reorder the terms for easier multiplication: 94.9536 = 6.28r2 + 2 * 3.14 * 1.8r Multiply 2 * 3.14 94.9536 = 6.28r2 + 6.28 * 1.8r Multiply 6.28 * 1.8 94.9536 = 6.28r2 + 11.304r Reorder the terms: 94.9536 = 11.304r + 6.28r2 Solving 94.9536 = 11.304r + 6.28r2 Solving for variable 'r'. Reorder the terms: 94.9536 + -11.304r + -6.28r2 = 11.304r + -11.304r + 6.28r2 + -6.28r2 Combine like terms: 11.304r + -11.304r = 0.000 94.9536 + -11.304r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 94.9536 + -11.304r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 94.9536 + -11.304r + -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'. -15.12 + 1.8r + r2 = 0 Move the constant term to the right: Add '15.12' to each side of the equation. -15.12 + 1.8r + 15.12 + r2 = 0 + 15.12 Reorder the terms: -15.12 + 15.12 + 1.8r + r2 = 0 + 15.12 Combine like terms: -15.12 + 15.12 = 0.00 0.00 + 1.8r + r2 = 0 + 15.12 1.8r + r2 = 0 + 15.12 Combine like terms: 0 + 15.12 = 15.12 1.8r + r2 = 15.12 The r term is 1.8r. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8r + 0.81 + r2 = 15.12 + 0.81 Reorder the terms: 0.81 + 1.8r + r2 = 15.12 + 0.81 Combine like terms: 15.12 + 0.81 = 15.93 0.81 + 1.8r + r2 = 15.93 Factor a perfect square on the left side: (r + 0.9)(r + 0.9) = 15.93 Calculate the square root of the right side: 3.991240409 Break this problem into two subproblems by setting (r + 0.9) equal to 3.991240409 and -3.991240409.Subproblem 1
r + 0.9 = 3.991240409 Simplifying r + 0.9 = 3.991240409 Reorder the terms: 0.9 + r = 3.991240409 Solving 0.9 + r = 3.991240409 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + r = 3.991240409 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + r = 3.991240409 + -0.9 r = 3.991240409 + -0.9 Combine like terms: 3.991240409 + -0.9 = 3.091240409 r = 3.091240409 Simplifying r = 3.091240409Subproblem 2
r + 0.9 = -3.991240409 Simplifying r + 0.9 = -3.991240409 Reorder the terms: 0.9 + r = -3.991240409 Solving 0.9 + r = -3.991240409 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + r = -3.991240409 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + r = -3.991240409 + -0.9 r = -3.991240409 + -0.9 Combine like terms: -3.991240409 + -0.9 = -4.891240409 r = -4.891240409 Simplifying r = -4.891240409Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.091240409, -4.891240409}
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