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Simplifying 1270.44 = 2 * 3.14r2 + 2 * 3.14r * 21.9 Multiply 2 * 3.14 1270.44 = 6.28r2 + 2 * 3.14r * 21.9 Reorder the terms for easier multiplication: 1270.44 = 6.28r2 + 2 * 3.14 * 21.9r Multiply 2 * 3.14 1270.44 = 6.28r2 + 6.28 * 21.9r Multiply 6.28 * 21.9 1270.44 = 6.28r2 + 137.532r Reorder the terms: 1270.44 = 137.532r + 6.28r2 Solving 1270.44 = 137.532r + 6.28r2 Solving for variable 'r'. Reorder the terms: 1270.44 + -137.532r + -6.28r2 = 137.532r + -137.532r + 6.28r2 + -6.28r2 Combine like terms: 137.532r + -137.532r = 0.000 1270.44 + -137.532r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 1270.44 + -137.532r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 1270.44 + -137.532r + -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'. -202.2993631 + 21.9r + r2 = 0 Move the constant term to the right: Add '202.2993631' to each side of the equation. -202.2993631 + 21.9r + 202.2993631 + r2 = 0 + 202.2993631 Reorder the terms: -202.2993631 + 202.2993631 + 21.9r + r2 = 0 + 202.2993631 Combine like terms: -202.2993631 + 202.2993631 = 0.0000000 0.0000000 + 21.9r + r2 = 0 + 202.2993631 21.9r + r2 = 0 + 202.2993631 Combine like terms: 0 + 202.2993631 = 202.2993631 21.9r + r2 = 202.2993631 The r term is 21.9r. Take half its coefficient (10.95). Square it (119.9025) and add it to both sides. Add '119.9025' to each side of the equation. 21.9r + 119.9025 + r2 = 202.2993631 + 119.9025 Reorder the terms: 119.9025 + 21.9r + r2 = 202.2993631 + 119.9025 Combine like terms: 202.2993631 + 119.9025 = 322.2018631 119.9025 + 21.9r + r2 = 322.2018631 Factor a perfect square on the left side: (r + 10.95)(r + 10.95) = 322.2018631 Calculate the square root of the right side: 17.949982259 Break this problem into two subproblems by setting (r + 10.95) equal to 17.949982259 and -17.949982259.Subproblem 1
r + 10.95 = 17.949982259 Simplifying r + 10.95 = 17.949982259 Reorder the terms: 10.95 + r = 17.949982259 Solving 10.95 + r = 17.949982259 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10.95' to each side of the equation. 10.95 + -10.95 + r = 17.949982259 + -10.95 Combine like terms: 10.95 + -10.95 = 0.00 0.00 + r = 17.949982259 + -10.95 r = 17.949982259 + -10.95 Combine like terms: 17.949982259 + -10.95 = 6.999982259 r = 6.999982259 Simplifying r = 6.999982259Subproblem 2
r + 10.95 = -17.949982259 Simplifying r + 10.95 = -17.949982259 Reorder the terms: 10.95 + r = -17.949982259 Solving 10.95 + r = -17.949982259 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10.95' to each side of the equation. 10.95 + -10.95 + r = -17.949982259 + -10.95 Combine like terms: 10.95 + -10.95 = 0.00 0.00 + r = -17.949982259 + -10.95 r = -17.949982259 + -10.95 Combine like terms: -17.949982259 + -10.95 = -28.899982259 r = -28.899982259 Simplifying r = -28.899982259Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.999982259, -28.899982259}
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