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Simplifying r2 + -20r + 91 = 8 Reorder the terms: 91 + -20r + r2 = 8 Solving 91 + -20r + r2 = 8 Solving for variable 'r'. Reorder the terms: 91 + -8 + -20r + r2 = 8 + -8 Combine like terms: 91 + -8 = 83 83 + -20r + r2 = 8 + -8 Combine like terms: 8 + -8 = 0 83 + -20r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-83' to each side of the equation. 83 + -20r + -83 + r2 = 0 + -83 Reorder the terms: 83 + -83 + -20r + r2 = 0 + -83 Combine like terms: 83 + -83 = 0 0 + -20r + r2 = 0 + -83 -20r + r2 = 0 + -83 Combine like terms: 0 + -83 = -83 -20r + r2 = -83 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 = -83 + 100 Reorder the terms: 100 + -20r + r2 = -83 + 100 Combine like terms: -83 + 100 = 17 100 + -20r + r2 = 17 Factor a perfect square on the left side: (r + -10)(r + -10) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (r + -10) equal to 4.123105626 and -4.123105626.Subproblem 1
r + -10 = 4.123105626 Simplifying r + -10 = 4.123105626 Reorder the terms: -10 + r = 4.123105626 Solving -10 + r = 4.123105626 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 = 4.123105626 + 10 Combine like terms: -10 + 10 = 0 0 + r = 4.123105626 + 10 r = 4.123105626 + 10 Combine like terms: 4.123105626 + 10 = 14.123105626 r = 14.123105626 Simplifying r = 14.123105626Subproblem 2
r + -10 = -4.123105626 Simplifying r + -10 = -4.123105626 Reorder the terms: -10 + r = -4.123105626 Solving -10 + r = -4.123105626 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 = -4.123105626 + 10 Combine like terms: -10 + 10 = 0 0 + r = -4.123105626 + 10 r = -4.123105626 + 10 Combine like terms: -4.123105626 + 10 = 5.876894374 r = 5.876894374 Simplifying r = 5.876894374Solution
The solution to the problem is based on the solutions from the subproblems. r = {14.123105626, 5.876894374}
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