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Simplifying r2 + -6r + 2 = 0 Reorder the terms: 2 + -6r + r2 = 0 Solving 2 + -6r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6r + -2 + r2 = 0 + -2 Reorder the terms: 2 + -2 + -6r + r2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6r + r2 = 0 + -2 -6r + r2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6r + r2 = -2 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 = -2 + 9 Reorder the terms: 9 + -6r + r2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6r + r2 = 7 Factor a perfect square on the left side: (r + -3)(r + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (r + -3) equal to 2.645751311 and -2.645751311.Subproblem 1
r + -3 = 2.645751311 Simplifying r + -3 = 2.645751311 Reorder the terms: -3 + r = 2.645751311 Solving -3 + r = 2.645751311 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 = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + r = 2.645751311 + 3 r = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 r = 5.645751311 Simplifying r = 5.645751311Subproblem 2
r + -3 = -2.645751311 Simplifying r + -3 = -2.645751311 Reorder the terms: -3 + r = -2.645751311 Solving -3 + r = -2.645751311 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 = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + r = -2.645751311 + 3 r = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 r = 0.354248689 Simplifying r = 0.354248689Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.645751311, 0.354248689}
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