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Simplifying r2 + -20r + 41 = 0 Reorder the terms: 41 + -20r + r2 = 0 Solving 41 + -20r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + -20r + -41 + r2 = 0 + -41 Reorder the terms: 41 + -41 + -20r + r2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -20r + r2 = 0 + -41 -20r + r2 = 0 + -41 Combine like terms: 0 + -41 = -41 -20r + r2 = -41 The r term is -20r. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20r + 100 + r2 = -41 + 100 Reorder the terms: 100 + -20r + r2 = -41 + 100 Combine like terms: -41 + 100 = 59 100 + -20r + r2 = 59 Factor a perfect square on the left side: (r + -10)(r + -10) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (r + -10) equal to 7.681145748 and -7.681145748.Subproblem 1
r + -10 = 7.681145748 Simplifying r + -10 = 7.681145748 Reorder the terms: -10 + r = 7.681145748 Solving -10 + r = 7.681145748 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = 7.681145748 + 10 Combine like terms: -10 + 10 = 0 0 + r = 7.681145748 + 10 r = 7.681145748 + 10 Combine like terms: 7.681145748 + 10 = 17.681145748 r = 17.681145748 Simplifying r = 17.681145748Subproblem 2
r + -10 = -7.681145748 Simplifying r + -10 = -7.681145748 Reorder the terms: -10 + r = -7.681145748 Solving -10 + r = -7.681145748 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = -7.681145748 + 10 Combine like terms: -10 + 10 = 0 0 + r = -7.681145748 + 10 r = -7.681145748 + 10 Combine like terms: -7.681145748 + 10 = 2.318854252 r = 2.318854252 Simplifying r = 2.318854252Solution
The solution to the problem is based on the solutions from the subproblems. r = {17.681145748, 2.318854252}
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