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Simplifying 1055 = 2 * 3.14r * 22 + 2 * 3.14r2 Reorder the terms for easier multiplication: 1055 = 2 * 3.14 * 22r + 2 * 3.14r2 Multiply 2 * 3.14 1055 = 6.28 * 22r + 2 * 3.14r2 Multiply 6.28 * 22 1055 = 138.16r + 2 * 3.14r2 Multiply 2 * 3.14 1055 = 138.16r + 6.28r2 Solving 1055 = 138.16r + 6.28r2 Solving for variable 'r'. Reorder the terms: 1055 + -138.16r + -6.28r2 = 138.16r + -138.16r + 6.28r2 + -6.28r2 Combine like terms: 138.16r + -138.16r = 0.00 1055 + -138.16r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 1055 + -138.16r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 1055 + -138.16r + -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'. -167.9936306 + 22r + r2 = 0 Move the constant term to the right: Add '167.9936306' to each side of the equation. -167.9936306 + 22r + 167.9936306 + r2 = 0 + 167.9936306 Reorder the terms: -167.9936306 + 167.9936306 + 22r + r2 = 0 + 167.9936306 Combine like terms: -167.9936306 + 167.9936306 = 0.0000000 0.0000000 + 22r + r2 = 0 + 167.9936306 22r + r2 = 0 + 167.9936306 Combine like terms: 0 + 167.9936306 = 167.9936306 22r + r2 = 167.9936306 The r term is 22r. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22r + 121 + r2 = 167.9936306 + 121 Reorder the terms: 121 + 22r + r2 = 167.9936306 + 121 Combine like terms: 167.9936306 + 121 = 288.9936306 121 + 22r + r2 = 288.9936306 Factor a perfect square on the left side: (r + 11)(r + 11) = 288.9936306 Calculate the square root of the right side: 16.999812664 Break this problem into two subproblems by setting (r + 11) equal to 16.999812664 and -16.999812664.Subproblem 1
r + 11 = 16.999812664 Simplifying r + 11 = 16.999812664 Reorder the terms: 11 + r = 16.999812664 Solving 11 + r = 16.999812664 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + r = 16.999812664 + -11 Combine like terms: 11 + -11 = 0 0 + r = 16.999812664 + -11 r = 16.999812664 + -11 Combine like terms: 16.999812664 + -11 = 5.999812664 r = 5.999812664 Simplifying r = 5.999812664Subproblem 2
r + 11 = -16.999812664 Simplifying r + 11 = -16.999812664 Reorder the terms: 11 + r = -16.999812664 Solving 11 + r = -16.999812664 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + r = -16.999812664 + -11 Combine like terms: 11 + -11 = 0 0 + r = -16.999812664 + -11 r = -16.999812664 + -11 Combine like terms: -16.999812664 + -11 = -27.999812664 r = -27.999812664 Simplifying r = -27.999812664Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.999812664, -27.999812664}
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