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Simplifying 9r + 9r2 + -2 = 0 Reorder the terms: -2 + 9r + 9r2 = 0 Solving -2 + 9r + 9r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + r + r2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + r + 0.2222222222 + r2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + r + r2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + r + r2 = 0 + 0.2222222222 r + r2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 r + r2 = 0.2222222222 The r term is r. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + r2 = 0.2222222222 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + r2 = 0.2222222222 + 0.25 Combine like terms: 0.2222222222 + 0.25 = 0.4722222222 1.25 + r2 = 0.4722222222 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = 0.4722222222 Calculate the square root of the right side: 0.687184271 Break this problem into two subproblems by setting (r + 0.5) equal to 0.687184271 and -0.687184271.Subproblem 1
r + 0.5 = 0.687184271 Simplifying r + 0.5 = 0.687184271 Reorder the terms: 0.5 + r = 0.687184271 Solving 0.5 + r = 0.687184271 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = 0.687184271 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = 0.687184271 + -0.5 r = 0.687184271 + -0.5 Combine like terms: 0.687184271 + -0.5 = 0.187184271 r = 0.187184271 Simplifying r = 0.187184271Subproblem 2
r + 0.5 = -0.687184271 Simplifying r + 0.5 = -0.687184271 Reorder the terms: 0.5 + r = -0.687184271 Solving 0.5 + r = -0.687184271 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + r = -0.687184271 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + r = -0.687184271 + -0.5 r = -0.687184271 + -0.5 Combine like terms: -0.687184271 + -0.5 = -1.187184271 r = -1.187184271 Simplifying r = -1.187184271Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.187184271, -1.187184271}
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