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Simplifying 25 = 17r + -1r2 Solving 25 = 17r + -1r2 Solving for variable 'r'. Reorder the terms: 25 + -17r + r2 = 17r + -17r + -1r2 + r2 Combine like terms: 17r + -17r = 0 25 + -17r + r2 = 0 + -1r2 + r2 25 + -17r + r2 = -1r2 + r2 Combine like terms: -1r2 + r2 = 0 25 + -17r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -17r + -25 + r2 = 0 + -25 Reorder the terms: 25 + -25 + -17r + r2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -17r + r2 = 0 + -25 -17r + r2 = 0 + -25 Combine like terms: 0 + -25 = -25 -17r + r2 = -25 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 = -25 + 72.25 Reorder the terms: 72.25 + -17r + r2 = -25 + 72.25 Combine like terms: -25 + 72.25 = 47.25 72.25 + -17r + r2 = 47.25 Factor a perfect square on the left side: (r + -8.5)(r + -8.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (r + -8.5) equal to 6.873863542 and -6.873863542.Subproblem 1
r + -8.5 = 6.873863542 Simplifying r + -8.5 = 6.873863542 Reorder the terms: -8.5 + r = 6.873863542 Solving -8.5 + r = 6.873863542 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 = 6.873863542 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + r = 6.873863542 + 8.5 r = 6.873863542 + 8.5 Combine like terms: 6.873863542 + 8.5 = 15.373863542 r = 15.373863542 Simplifying r = 15.373863542Subproblem 2
r + -8.5 = -6.873863542 Simplifying r + -8.5 = -6.873863542 Reorder the terms: -8.5 + r = -6.873863542 Solving -8.5 + r = -6.873863542 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 = -6.873863542 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + r = -6.873863542 + 8.5 r = -6.873863542 + 8.5 Combine like terms: -6.873863542 + 8.5 = 1.626136458 r = 1.626136458 Simplifying r = 1.626136458Solution
The solution to the problem is based on the solutions from the subproblems. r = {15.373863542, 1.626136458}
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