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Simplifying 5r(r + 6) + -9 = 0 Reorder the terms: 5r(6 + r) + -9 = 0 (6 * 5r + r * 5r) + -9 = 0 (30r + 5r2) + -9 = 0 Reorder the terms: -9 + 30r + 5r2 = 0 Solving -9 + 30r + 5r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 6r + r2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 6r + 1.8 + r2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 6r + r2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 6r + r2 = 0 + 1.8 6r + r2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 6r + r2 = 1.8 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 = 1.8 + 9 Reorder the terms: 9 + 6r + r2 = 1.8 + 9 Combine like terms: 1.8 + 9 = 10.8 9 + 6r + r2 = 10.8 Factor a perfect square on the left side: (r + 3)(r + 3) = 10.8 Calculate the square root of the right side: 3.286335345 Break this problem into two subproblems by setting (r + 3) equal to 3.286335345 and -3.286335345.Subproblem 1
r + 3 = 3.286335345 Simplifying r + 3 = 3.286335345 Reorder the terms: 3 + r = 3.286335345 Solving 3 + r = 3.286335345 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 = 3.286335345 + -3 Combine like terms: 3 + -3 = 0 0 + r = 3.286335345 + -3 r = 3.286335345 + -3 Combine like terms: 3.286335345 + -3 = 0.286335345 r = 0.286335345 Simplifying r = 0.286335345Subproblem 2
r + 3 = -3.286335345 Simplifying r + 3 = -3.286335345 Reorder the terms: 3 + r = -3.286335345 Solving 3 + r = -3.286335345 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 = -3.286335345 + -3 Combine like terms: 3 + -3 = 0 0 + r = -3.286335345 + -3 r = -3.286335345 + -3 Combine like terms: -3.286335345 + -3 = -6.286335345 r = -6.286335345 Simplifying r = -6.286335345Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.286335345, -6.286335345}
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