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Simplifying r2 + 4r + -2500 = 0 Reorder the terms: -2500 + 4r + r2 = 0 Solving -2500 + 4r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '2500' to each side of the equation. -2500 + 4r + 2500 + r2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 4r + r2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 4r + r2 = 0 + 2500 4r + r2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 4r + r2 = 2500 The r term is 4r. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4r + 4 + r2 = 2500 + 4 Reorder the terms: 4 + 4r + r2 = 2500 + 4 Combine like terms: 2500 + 4 = 2504 4 + 4r + r2 = 2504 Factor a perfect square on the left side: (r + 2)(r + 2) = 2504 Calculate the square root of the right side: 50.039984013 Break this problem into two subproblems by setting (r + 2) equal to 50.039984013 and -50.039984013.Subproblem 1
r + 2 = 50.039984013 Simplifying r + 2 = 50.039984013 Reorder the terms: 2 + r = 50.039984013 Solving 2 + r = 50.039984013 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 50.039984013 + -2 Combine like terms: 2 + -2 = 0 0 + r = 50.039984013 + -2 r = 50.039984013 + -2 Combine like terms: 50.039984013 + -2 = 48.039984013 r = 48.039984013 Simplifying r = 48.039984013Subproblem 2
r + 2 = -50.039984013 Simplifying r + 2 = -50.039984013 Reorder the terms: 2 + r = -50.039984013 Solving 2 + r = -50.039984013 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -50.039984013 + -2 Combine like terms: 2 + -2 = 0 0 + r = -50.039984013 + -2 r = -50.039984013 + -2 Combine like terms: -50.039984013 + -2 = -52.039984013 r = -52.039984013 Simplifying r = -52.039984013Solution
The solution to the problem is based on the solutions from the subproblems. r = {48.039984013, -52.039984013}
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