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Simplifying 17r + r2 = 52 Solving 17r + r2 = 52 Solving for variable 'r'. Reorder the terms: -52 + 17r + r2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 17r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 17r + 52 + r2 = 0 + 52 Reorder the terms: -52 + 52 + 17r + r2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 17r + r2 = 0 + 52 17r + r2 = 0 + 52 Combine like terms: 0 + 52 = 52 17r + r2 = 52 The r term is 17r. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17r + 72.25 + r2 = 52 + 72.25 Reorder the terms: 72.25 + 17r + r2 = 52 + 72.25 Combine like terms: 52 + 72.25 = 124.25 72.25 + 17r + r2 = 124.25 Factor a perfect square on the left side: (r + 8.5)(r + 8.5) = 124.25 Calculate the square root of the right side: 11.146748405 Break this problem into two subproblems by setting (r + 8.5) equal to 11.146748405 and -11.146748405.Subproblem 1
r + 8.5 = 11.146748405 Simplifying r + 8.5 = 11.146748405 Reorder the terms: 8.5 + r = 11.146748405 Solving 8.5 + r = 11.146748405 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + r = 11.146748405 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + r = 11.146748405 + -8.5 r = 11.146748405 + -8.5 Combine like terms: 11.146748405 + -8.5 = 2.646748405 r = 2.646748405 Simplifying r = 2.646748405Subproblem 2
r + 8.5 = -11.146748405 Simplifying r + 8.5 = -11.146748405 Reorder the terms: 8.5 + r = -11.146748405 Solving 8.5 + r = -11.146748405 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + r = -11.146748405 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + r = -11.146748405 + -8.5 r = -11.146748405 + -8.5 Combine like terms: -11.146748405 + -8.5 = -19.646748405 r = -19.646748405 Simplifying r = -19.646748405Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.646748405, -19.646748405}
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