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Simplifying 11r2 + -58r + -396 = 0 Reorder the terms: -396 + -58r + 11r2 = 0 Solving -396 + -58r + 11r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -36 + -5.272727273r + r2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -5.272727273r + 36 + r2 = 0 + 36 Reorder the terms: -36 + 36 + -5.272727273r + r2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -5.272727273r + r2 = 0 + 36 -5.272727273r + r2 = 0 + 36 Combine like terms: 0 + 36 = 36 -5.272727273r + r2 = 36 The r term is -5.272727273r. Take half its coefficient (-2.636363637). Square it (6.950413227) and add it to both sides. Add '6.950413227' to each side of the equation. -5.272727273r + 6.950413227 + r2 = 36 + 6.950413227 Reorder the terms: 6.950413227 + -5.272727273r + r2 = 36 + 6.950413227 Combine like terms: 36 + 6.950413227 = 42.950413227 6.950413227 + -5.272727273r + r2 = 42.950413227 Factor a perfect square on the left side: (r + -2.636363637)(r + -2.636363637) = 42.950413227 Calculate the square root of the right side: 6.553656478 Break this problem into two subproblems by setting (r + -2.636363637) equal to 6.553656478 and -6.553656478.Subproblem 1
r + -2.636363637 = 6.553656478 Simplifying r + -2.636363637 = 6.553656478 Reorder the terms: -2.636363637 + r = 6.553656478 Solving -2.636363637 + r = 6.553656478 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.636363637' to each side of the equation. -2.636363637 + 2.636363637 + r = 6.553656478 + 2.636363637 Combine like terms: -2.636363637 + 2.636363637 = 0.000000000 0.000000000 + r = 6.553656478 + 2.636363637 r = 6.553656478 + 2.636363637 Combine like terms: 6.553656478 + 2.636363637 = 9.190020115 r = 9.190020115 Simplifying r = 9.190020115Subproblem 2
r + -2.636363637 = -6.553656478 Simplifying r + -2.636363637 = -6.553656478 Reorder the terms: -2.636363637 + r = -6.553656478 Solving -2.636363637 + r = -6.553656478 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.636363637' to each side of the equation. -2.636363637 + 2.636363637 + r = -6.553656478 + 2.636363637 Combine like terms: -2.636363637 + 2.636363637 = 0.000000000 0.000000000 + r = -6.553656478 + 2.636363637 r = -6.553656478 + 2.636363637 Combine like terms: -6.553656478 + 2.636363637 = -3.917292841 r = -3.917292841 Simplifying r = -3.917292841Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.190020115, -3.917292841}
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