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Simplifying 0 = 6.28r2 + 404.432r + -7009.2336 Reorder the terms: 0 = -7009.2336 + 404.432r + 6.28r2 Solving 0 = -7009.2336 + 404.432r + 6.28r2 Solving for variable 'r'. Combine like terms: 0 + 7009.2336 = 7009.2336 7009.2336 + -404.432r + -6.28r2 = -7009.2336 + 404.432r + 6.28r2 + 7009.2336 + -404.432r + -6.28r2 Reorder the terms: 7009.2336 + -404.432r + -6.28r2 = -7009.2336 + 7009.2336 + 404.432r + -404.432r + 6.28r2 + -6.28r2 Combine like terms: -7009.2336 + 7009.2336 = 0.0000 7009.2336 + -404.432r + -6.28r2 = 0.0000 + 404.432r + -404.432r + 6.28r2 + -6.28r2 7009.2336 + -404.432r + -6.28r2 = 404.432r + -404.432r + 6.28r2 + -6.28r2 Combine like terms: 404.432r + -404.432r = 0.000 7009.2336 + -404.432r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 7009.2336 + -404.432r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 7009.2336 + -404.432r + -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'. -1116.12 + 64.4r + r2 = 0 Move the constant term to the right: Add '1116.12' to each side of the equation. -1116.12 + 64.4r + 1116.12 + r2 = 0 + 1116.12 Reorder the terms: -1116.12 + 1116.12 + 64.4r + r2 = 0 + 1116.12 Combine like terms: -1116.12 + 1116.12 = 0.00 0.00 + 64.4r + r2 = 0 + 1116.12 64.4r + r2 = 0 + 1116.12 Combine like terms: 0 + 1116.12 = 1116.12 64.4r + r2 = 1116.12 The r term is 64.4r. Take half its coefficient (32.2). Square it (1036.84) and add it to both sides. Add '1036.84' to each side of the equation. 64.4r + 1036.84 + r2 = 1116.12 + 1036.84 Reorder the terms: 1036.84 + 64.4r + r2 = 1116.12 + 1036.84 Combine like terms: 1116.12 + 1036.84 = 2152.96 1036.84 + 64.4r + r2 = 2152.96 Factor a perfect square on the left side: (r + 32.2)(r + 32.2) = 2152.96 Calculate the square root of the right side: 46.4 Break this problem into two subproblems by setting (r + 32.2) equal to 46.4 and -46.4.Subproblem 1
r + 32.2 = 46.4 Simplifying r + 32.2 = 46.4 Reorder the terms: 32.2 + r = 46.4 Solving 32.2 + r = 46.4 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-32.2' to each side of the equation. 32.2 + -32.2 + r = 46.4 + -32.2 Combine like terms: 32.2 + -32.2 = 0.0 0.0 + r = 46.4 + -32.2 r = 46.4 + -32.2 Combine like terms: 46.4 + -32.2 = 14.2 r = 14.2 Simplifying r = 14.2Subproblem 2
r + 32.2 = -46.4 Simplifying r + 32.2 = -46.4 Reorder the terms: 32.2 + r = -46.4 Solving 32.2 + r = -46.4 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-32.2' to each side of the equation. 32.2 + -32.2 + r = -46.4 + -32.2 Combine like terms: 32.2 + -32.2 = 0.0 0.0 + r = -46.4 + -32.2 r = -46.4 + -32.2 Combine like terms: -46.4 + -32.2 = -78.6 r = -78.6 Simplifying r = -78.6Solution
The solution to the problem is based on the solutions from the subproblems. r = {14.2, -78.6}
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