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Simplifying r2 + 10r = 1 Reorder the terms: 10r + r2 = 1 Solving 10r + r2 = 1 Solving for variable 'r'. Reorder the terms: -1 + 10r + r2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 10r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 10r + 1 + r2 = 0 + 1 Reorder the terms: -1 + 1 + 10r + r2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 10r + r2 = 0 + 1 10r + r2 = 0 + 1 Combine like terms: 0 + 1 = 1 10r + r2 = 1 The r term is 10r. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10r + 25 + r2 = 1 + 25 Reorder the terms: 25 + 10r + r2 = 1 + 25 Combine like terms: 1 + 25 = 26 25 + 10r + r2 = 26 Factor a perfect square on the left side: (r + 5)(r + 5) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (r + 5) equal to 5.099019514 and -5.099019514.Subproblem 1
r + 5 = 5.099019514 Simplifying r + 5 = 5.099019514 Reorder the terms: 5 + r = 5.099019514 Solving 5 + r = 5.099019514 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 5.099019514 + -5 Combine like terms: 5 + -5 = 0 0 + r = 5.099019514 + -5 r = 5.099019514 + -5 Combine like terms: 5.099019514 + -5 = 0.099019514 r = 0.099019514 Simplifying r = 0.099019514Subproblem 2
r + 5 = -5.099019514 Simplifying r + 5 = -5.099019514 Reorder the terms: 5 + r = -5.099019514 Solving 5 + r = -5.099019514 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = -5.099019514 + -5 Combine like terms: 5 + -5 = 0 0 + r = -5.099019514 + -5 r = -5.099019514 + -5 Combine like terms: -5.099019514 + -5 = -10.099019514 r = -10.099019514 Simplifying r = -10.099019514Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.099019514, -10.099019514}
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