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Simplifying 0.09r2 + 2.44r = 9.03 Reorder the terms: 2.44r + 0.09r2 = 9.03 Solving 2.44r + 0.09r2 = 9.03 Solving for variable 'r'. Reorder the terms: -9.03 + 2.44r + 0.09r2 = 9.03 + -9.03 Combine like terms: 9.03 + -9.03 = 0.00 -9.03 + 2.44r + 0.09r2 = 0.00 Begin completing the square. Divide all terms by 0.09 the coefficient of the squared term: Divide each side by '0.09'. -100.3333333 + 27.11111111r + r2 = 0 Move the constant term to the right: Add '100.3333333' to each side of the equation. -100.3333333 + 27.11111111r + 100.3333333 + r2 = 0 + 100.3333333 Reorder the terms: -100.3333333 + 100.3333333 + 27.11111111r + r2 = 0 + 100.3333333 Combine like terms: -100.3333333 + 100.3333333 = 0.0000000 0.0000000 + 27.11111111r + r2 = 0 + 100.3333333 27.11111111r + r2 = 0 + 100.3333333 Combine like terms: 0 + 100.3333333 = 100.3333333 27.11111111r + r2 = 100.3333333 The r term is 27.11111111r. Take half its coefficient (13.55555556). Square it (183.7530865) and add it to both sides. Add '183.7530865' to each side of the equation. 27.11111111r + 183.7530865 + r2 = 100.3333333 + 183.7530865 Reorder the terms: 183.7530865 + 27.11111111r + r2 = 100.3333333 + 183.7530865 Combine like terms: 100.3333333 + 183.7530865 = 284.0864198 183.7530865 + 27.11111111r + r2 = 284.0864198 Factor a perfect square on the left side: (r + 13.55555556)(r + 13.55555556) = 284.0864198 Calculate the square root of the right side: 16.854863387 Break this problem into two subproblems by setting (r + 13.55555556) equal to 16.854863387 and -16.854863387.Subproblem 1
r + 13.55555556 = 16.854863387 Simplifying r + 13.55555556 = 16.854863387 Reorder the terms: 13.55555556 + r = 16.854863387 Solving 13.55555556 + r = 16.854863387 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-13.55555556' to each side of the equation. 13.55555556 + -13.55555556 + r = 16.854863387 + -13.55555556 Combine like terms: 13.55555556 + -13.55555556 = 0.00000000 0.00000000 + r = 16.854863387 + -13.55555556 r = 16.854863387 + -13.55555556 Combine like terms: 16.854863387 + -13.55555556 = 3.299307827 r = 3.299307827 Simplifying r = 3.299307827Subproblem 2
r + 13.55555556 = -16.854863387 Simplifying r + 13.55555556 = -16.854863387 Reorder the terms: 13.55555556 + r = -16.854863387 Solving 13.55555556 + r = -16.854863387 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-13.55555556' to each side of the equation. 13.55555556 + -13.55555556 + r = -16.854863387 + -13.55555556 Combine like terms: 13.55555556 + -13.55555556 = 0.00000000 0.00000000 + r = -16.854863387 + -13.55555556 r = -16.854863387 + -13.55555556 Combine like terms: -16.854863387 + -13.55555556 = -30.410418947 r = -30.410418947 Simplifying r = -30.410418947Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.299307827, -30.410418947}
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