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Simplifying 16616.88 = 2 * 3.14r * 105 + 2 * 3.14r * r Reorder the terms for easier multiplication: 16616.88 = 2 * 3.14 * 105r + 2 * 3.14r * r Multiply 2 * 3.14 16616.88 = 6.28 * 105r + 2 * 3.14r * r Multiply 6.28 * 105 16616.88 = 659.4r + 2 * 3.14r * r Multiply 2 * 3.14 16616.88 = 659.4r + 6.28r * r Multiply r * r 16616.88 = 659.4r + 6.28r2 Solving 16616.88 = 659.4r + 6.28r2 Solving for variable 'r'. Reorder the terms: 16616.88 + -659.4r + -6.28r2 = 659.4r + -659.4r + 6.28r2 + -6.28r2 Combine like terms: 659.4r + -659.4r = 0.0 16616.88 + -659.4r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2 16616.88 + -659.4r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 16616.88 + -659.4r + -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'. -2646 + 105r + r2 = 0 Move the constant term to the right: Add '2646' to each side of the equation. -2646 + 105r + 2646 + r2 = 0 + 2646 Reorder the terms: -2646 + 2646 + 105r + r2 = 0 + 2646 Combine like terms: -2646 + 2646 = 0 0 + 105r + r2 = 0 + 2646 105r + r2 = 0 + 2646 Combine like terms: 0 + 2646 = 2646 105r + r2 = 2646 The r term is 105r. Take half its coefficient (52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. 105r + 2756.25 + r2 = 2646 + 2756.25 Reorder the terms: 2756.25 + 105r + r2 = 2646 + 2756.25 Combine like terms: 2646 + 2756.25 = 5402.25 2756.25 + 105r + r2 = 5402.25 Factor a perfect square on the left side: (r + 52.5)(r + 52.5) = 5402.25 Calculate the square root of the right side: 73.5 Break this problem into two subproblems by setting (r + 52.5) equal to 73.5 and -73.5.Subproblem 1
r + 52.5 = 73.5 Simplifying r + 52.5 = 73.5 Reorder the terms: 52.5 + r = 73.5 Solving 52.5 + r = 73.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + r = 73.5 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + r = 73.5 + -52.5 r = 73.5 + -52.5 Combine like terms: 73.5 + -52.5 = 21 r = 21 Simplifying r = 21Subproblem 2
r + 52.5 = -73.5 Simplifying r + 52.5 = -73.5 Reorder the terms: 52.5 + r = -73.5 Solving 52.5 + r = -73.5 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + r = -73.5 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + r = -73.5 + -52.5 r = -73.5 + -52.5 Combine like terms: -73.5 + -52.5 = -126 r = -126 Simplifying r = -126Solution
The solution to the problem is based on the solutions from the subproblems. r = {21, -126}
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