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Simplifying r2 + 5r + -96 = 0 Reorder the terms: -96 + 5r + r2 = 0 Solving -96 + 5r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + 5r + 96 + r2 = 0 + 96 Reorder the terms: -96 + 96 + 5r + r2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 5r + r2 = 0 + 96 5r + r2 = 0 + 96 Combine like terms: 0 + 96 = 96 5r + r2 = 96 The r term is 5r. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5r + 6.25 + r2 = 96 + 6.25 Reorder the terms: 6.25 + 5r + r2 = 96 + 6.25 Combine like terms: 96 + 6.25 = 102.25 6.25 + 5r + r2 = 102.25 Factor a perfect square on the left side: (r + 2.5)(r + 2.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (r + 2.5) equal to 10.111874208 and -10.111874208.Subproblem 1
r + 2.5 = 10.111874208 Simplifying r + 2.5 = 10.111874208 Reorder the terms: 2.5 + r = 10.111874208 Solving 2.5 + r = 10.111874208 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = 10.111874208 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = 10.111874208 + -2.5 r = 10.111874208 + -2.5 Combine like terms: 10.111874208 + -2.5 = 7.611874208 r = 7.611874208 Simplifying r = 7.611874208Subproblem 2
r + 2.5 = -10.111874208 Simplifying r + 2.5 = -10.111874208 Reorder the terms: 2.5 + r = -10.111874208 Solving 2.5 + r = -10.111874208 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + r = -10.111874208 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = -10.111874208 + -2.5 r = -10.111874208 + -2.5 Combine like terms: -10.111874208 + -2.5 = -12.611874208 r = -12.611874208 Simplifying r = -12.611874208Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.611874208, -12.611874208}
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