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Simplifying 2r2 + -12r + 11 = 0 Reorder the terms: 11 + -12r + 2r2 = 0 Solving 11 + -12r + 2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + -6r + r2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -6r + -5.5 + r2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -6r + r2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -6r + r2 = 0 + -5.5 -6r + r2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -6r + r2 = -5.5 The r term is -6r. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6r + 9 + r2 = -5.5 + 9 Reorder the terms: 9 + -6r + r2 = -5.5 + 9 Combine like terms: -5.5 + 9 = 3.5 9 + -6r + r2 = 3.5 Factor a perfect square on the left side: (r + -3)(r + -3) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (r + -3) equal to 1.870828693 and -1.870828693.Subproblem 1
r + -3 = 1.870828693 Simplifying r + -3 = 1.870828693 Reorder the terms: -3 + r = 1.870828693 Solving -3 + r = 1.870828693 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = 1.870828693 + 3 Combine like terms: -3 + 3 = 0 0 + r = 1.870828693 + 3 r = 1.870828693 + 3 Combine like terms: 1.870828693 + 3 = 4.870828693 r = 4.870828693 Simplifying r = 4.870828693Subproblem 2
r + -3 = -1.870828693 Simplifying r + -3 = -1.870828693 Reorder the terms: -3 + r = -1.870828693 Solving -3 + r = -1.870828693 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = -1.870828693 + 3 Combine like terms: -3 + 3 = 0 0 + r = -1.870828693 + 3 r = -1.870828693 + 3 Combine like terms: -1.870828693 + 3 = 1.129171307 r = 1.129171307 Simplifying r = 1.129171307Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.870828693, 1.129171307}
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