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Simplifying r2 + -6r + -37 = 0 Reorder the terms: -37 + -6r + r2 = 0 Solving -37 + -6r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -6r + 37 + r2 = 0 + 37 Reorder the terms: -37 + 37 + -6r + r2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -6r + r2 = 0 + 37 -6r + r2 = 0 + 37 Combine like terms: 0 + 37 = 37 -6r + r2 = 37 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 = 37 + 9 Reorder the terms: 9 + -6r + r2 = 37 + 9 Combine like terms: 37 + 9 = 46 9 + -6r + r2 = 46 Factor a perfect square on the left side: (r + -3)(r + -3) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (r + -3) equal to 6.782329983 and -6.782329983.Subproblem 1
r + -3 = 6.782329983 Simplifying r + -3 = 6.782329983 Reorder the terms: -3 + r = 6.782329983 Solving -3 + r = 6.782329983 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 = 6.782329983 + 3 Combine like terms: -3 + 3 = 0 0 + r = 6.782329983 + 3 r = 6.782329983 + 3 Combine like terms: 6.782329983 + 3 = 9.782329983 r = 9.782329983 Simplifying r = 9.782329983Subproblem 2
r + -3 = -6.782329983 Simplifying r + -3 = -6.782329983 Reorder the terms: -3 + r = -6.782329983 Solving -3 + r = -6.782329983 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 = -6.782329983 + 3 Combine like terms: -3 + 3 = 0 0 + r = -6.782329983 + 3 r = -6.782329983 + 3 Combine like terms: -6.782329983 + 3 = -3.782329983 r = -3.782329983 Simplifying r = -3.782329983Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.782329983, -3.782329983}
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