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Simplifying 2r2 = -10 + 11r Solving 2r2 = -10 + 11r Solving for variable 'r'. Reorder the terms: 10 + -11r + 2r2 = -10 + 11r + 10 + -11r Reorder the terms: 10 + -11r + 2r2 = -10 + 10 + 11r + -11r Combine like terms: -10 + 10 = 0 10 + -11r + 2r2 = 0 + 11r + -11r 10 + -11r + 2r2 = 11r + -11r Combine like terms: 11r + -11r = 0 10 + -11r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + -5.5r + r2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -5.5r + -5 + r2 = 0 + -5 Reorder the terms: 5 + -5 + -5.5r + r2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5.5r + r2 = 0 + -5 -5.5r + r2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5.5r + r2 = -5 The r term is -5.5r. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5r + 7.5625 + r2 = -5 + 7.5625 Reorder the terms: 7.5625 + -5.5r + r2 = -5 + 7.5625 Combine like terms: -5 + 7.5625 = 2.5625 7.5625 + -5.5r + r2 = 2.5625 Factor a perfect square on the left side: (r + -2.75)(r + -2.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (r + -2.75) equal to 1.600781059 and -1.600781059.Subproblem 1
r + -2.75 = 1.600781059 Simplifying r + -2.75 = 1.600781059 Reorder the terms: -2.75 + r = 1.600781059 Solving -2.75 + r = 1.600781059 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + r = 1.600781059 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + r = 1.600781059 + 2.75 r = 1.600781059 + 2.75 Combine like terms: 1.600781059 + 2.75 = 4.350781059 r = 4.350781059 Simplifying r = 4.350781059Subproblem 2
r + -2.75 = -1.600781059 Simplifying r + -2.75 = -1.600781059 Reorder the terms: -2.75 + r = -1.600781059 Solving -2.75 + r = -1.600781059 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + r = -1.600781059 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + r = -1.600781059 + 2.75 r = -1.600781059 + 2.75 Combine like terms: -1.600781059 + 2.75 = 1.149218941 r = 1.149218941 Simplifying r = 1.149218941Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.350781059, 1.149218941}
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