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Simplifying 6r(r + 8) = 11 Reorder the terms: 6r(8 + r) = 11 (8 * 6r + r * 6r) = 11 (48r + 6r2) = 11 Solving 48r + 6r2 = 11 Solving for variable 'r'. Reorder the terms: -11 + 48r + 6r2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 48r + 6r2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + 8r + r2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + 8r + 1.833333333 + r2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + 8r + r2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + 8r + r2 = 0 + 1.833333333 8r + r2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 8r + r2 = 1.833333333 The r term is 8r. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8r + 16 + r2 = 1.833333333 + 16 Reorder the terms: 16 + 8r + r2 = 1.833333333 + 16 Combine like terms: 1.833333333 + 16 = 17.833333333 16 + 8r + r2 = 17.833333333 Factor a perfect square on the left side: (r + 4)(r + 4) = 17.833333333 Calculate the square root of the right side: 4.222953153 Break this problem into two subproblems by setting (r + 4) equal to 4.222953153 and -4.222953153.Subproblem 1
r + 4 = 4.222953153 Simplifying r + 4 = 4.222953153 Reorder the terms: 4 + r = 4.222953153 Solving 4 + r = 4.222953153 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = 4.222953153 + -4 Combine like terms: 4 + -4 = 0 0 + r = 4.222953153 + -4 r = 4.222953153 + -4 Combine like terms: 4.222953153 + -4 = 0.222953153 r = 0.222953153 Simplifying r = 0.222953153Subproblem 2
r + 4 = -4.222953153 Simplifying r + 4 = -4.222953153 Reorder the terms: 4 + r = -4.222953153 Solving 4 + r = -4.222953153 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = -4.222953153 + -4 Combine like terms: 4 + -4 = 0 0 + r = -4.222953153 + -4 r = -4.222953153 + -4 Combine like terms: -4.222953153 + -4 = -8.222953153 r = -8.222953153 Simplifying r = -8.222953153Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.222953153, -8.222953153}
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