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Simplifying r2 + 5r = 729 Reorder the terms: 5r + r2 = 729 Solving 5r + r2 = 729 Solving for variable 'r'. Reorder the terms: -729 + 5r + r2 = 729 + -729 Combine like terms: 729 + -729 = 0 -729 + 5r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '729' to each side of the equation. -729 + 5r + 729 + r2 = 0 + 729 Reorder the terms: -729 + 729 + 5r + r2 = 0 + 729 Combine like terms: -729 + 729 = 0 0 + 5r + r2 = 0 + 729 5r + r2 = 0 + 729 Combine like terms: 0 + 729 = 729 5r + r2 = 729 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 = 729 + 6.25 Reorder the terms: 6.25 + 5r + r2 = 729 + 6.25 Combine like terms: 729 + 6.25 = 735.25 6.25 + 5r + r2 = 735.25 Factor a perfect square on the left side: (r + 2.5)(r + 2.5) = 735.25 Calculate the square root of the right side: 27.115493726 Break this problem into two subproblems by setting (r + 2.5) equal to 27.115493726 and -27.115493726.Subproblem 1
r + 2.5 = 27.115493726 Simplifying r + 2.5 = 27.115493726 Reorder the terms: 2.5 + r = 27.115493726 Solving 2.5 + r = 27.115493726 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 = 27.115493726 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = 27.115493726 + -2.5 r = 27.115493726 + -2.5 Combine like terms: 27.115493726 + -2.5 = 24.615493726 r = 24.615493726 Simplifying r = 24.615493726Subproblem 2
r + 2.5 = -27.115493726 Simplifying r + 2.5 = -27.115493726 Reorder the terms: 2.5 + r = -27.115493726 Solving 2.5 + r = -27.115493726 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 = -27.115493726 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + r = -27.115493726 + -2.5 r = -27.115493726 + -2.5 Combine like terms: -27.115493726 + -2.5 = -29.615493726 r = -29.615493726 Simplifying r = -29.615493726Solution
The solution to the problem is based on the solutions from the subproblems. r = {24.615493726, -29.615493726}
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