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Simplifying 3 = 10r2 + 110r Reorder the terms: 3 = 110r + 10r2 Solving 3 = 110r + 10r2 Solving for variable 'r'. Reorder the terms: 3 + -110r + -10r2 = 110r + -110r + 10r2 + -10r2 Combine like terms: 110r + -110r = 0 3 + -110r + -10r2 = 0 + 10r2 + -10r2 3 + -110r + -10r2 = 10r2 + -10r2 Combine like terms: 10r2 + -10r2 = 0 3 + -110r + -10r2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.3 + 11r + r2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 11r + 0.3 + r2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 11r + r2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 11r + r2 = 0 + 0.3 11r + r2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 11r + r2 = 0.3 The r term is 11r. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11r + 30.25 + r2 = 0.3 + 30.25 Reorder the terms: 30.25 + 11r + r2 = 0.3 + 30.25 Combine like terms: 0.3 + 30.25 = 30.55 30.25 + 11r + r2 = 30.55 Factor a perfect square on the left side: (r + 5.5)(r + 5.5) = 30.55 Calculate the square root of the right side: 5.527205442 Break this problem into two subproblems by setting (r + 5.5) equal to 5.527205442 and -5.527205442.Subproblem 1
r + 5.5 = 5.527205442 Simplifying r + 5.5 = 5.527205442 Reorder the terms: 5.5 + r = 5.527205442 Solving 5.5 + r = 5.527205442 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + r = 5.527205442 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + r = 5.527205442 + -5.5 r = 5.527205442 + -5.5 Combine like terms: 5.527205442 + -5.5 = 0.027205442 r = 0.027205442 Simplifying r = 0.027205442Subproblem 2
r + 5.5 = -5.527205442 Simplifying r + 5.5 = -5.527205442 Reorder the terms: 5.5 + r = -5.527205442 Solving 5.5 + r = -5.527205442 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + r = -5.527205442 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + r = -5.527205442 + -5.5 r = -5.527205442 + -5.5 Combine like terms: -5.527205442 + -5.5 = -11.027205442 r = -11.027205442 Simplifying r = -11.027205442Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.027205442, -11.027205442}
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