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Simplifying r2 + 2r = 38 Reorder the terms: 2r + r2 = 38 Solving 2r + r2 = 38 Solving for variable 'r'. Reorder the terms: -38 + 2r + r2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + 2r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 2r + 38 + r2 = 0 + 38 Reorder the terms: -38 + 38 + 2r + r2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 2r + r2 = 0 + 38 2r + r2 = 0 + 38 Combine like terms: 0 + 38 = 38 2r + r2 = 38 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = 38 + 1 Reorder the terms: 1 + 2r + r2 = 38 + 1 Combine like terms: 38 + 1 = 39 1 + 2r + r2 = 39 Factor a perfect square on the left side: (r + 1)(r + 1) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (r + 1) equal to 6.244997998 and -6.244997998.Subproblem 1
r + 1 = 6.244997998 Simplifying r + 1 = 6.244997998 Reorder the terms: 1 + r = 6.244997998 Solving 1 + r = 6.244997998 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + r = 6.244997998 + -1 r = 6.244997998 + -1 Combine like terms: 6.244997998 + -1 = 5.244997998 r = 5.244997998 Simplifying r = 5.244997998Subproblem 2
r + 1 = -6.244997998 Simplifying r + 1 = -6.244997998 Reorder the terms: 1 + r = -6.244997998 Solving 1 + r = -6.244997998 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + r = -6.244997998 + -1 r = -6.244997998 + -1 Combine like terms: -6.244997998 + -1 = -7.244997998 r = -7.244997998 Simplifying r = -7.244997998Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.244997998, -7.244997998}
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