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Simplifying r2 + -6r = 17 Reorder the terms: -6r + r2 = 17 Solving -6r + r2 = 17 Solving for variable 'r'. Reorder the terms: -17 + -6r + r2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -6r + 17 + r2 = 0 + 17 Reorder the terms: -17 + 17 + -6r + r2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -6r + r2 = 0 + 17 -6r + r2 = 0 + 17 Combine like terms: 0 + 17 = 17 -6r + r2 = 17 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 = 17 + 9 Reorder the terms: 9 + -6r + r2 = 17 + 9 Combine like terms: 17 + 9 = 26 9 + -6r + r2 = 26 Factor a perfect square on the left side: (r + -3)(r + -3) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (r + -3) equal to 5.099019514 and -5.099019514.Subproblem 1
r + -3 = 5.099019514 Simplifying r + -3 = 5.099019514 Reorder the terms: -3 + r = 5.099019514 Solving -3 + r = 5.099019514 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 = 5.099019514 + 3 Combine like terms: -3 + 3 = 0 0 + r = 5.099019514 + 3 r = 5.099019514 + 3 Combine like terms: 5.099019514 + 3 = 8.099019514 r = 8.099019514 Simplifying r = 8.099019514Subproblem 2
r + -3 = -5.099019514 Simplifying r + -3 = -5.099019514 Reorder the terms: -3 + r = -5.099019514 Solving -3 + r = -5.099019514 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 = -5.099019514 + 3 Combine like terms: -3 + 3 = 0 0 + r = -5.099019514 + 3 r = -5.099019514 + 3 Combine like terms: -5.099019514 + 3 = -2.099019514 r = -2.099019514 Simplifying r = -2.099019514Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.099019514, -2.099019514}
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