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Simplifying r2 + -21r + -20 = 0 Reorder the terms: -20 + -21r + r2 = 0 Solving -20 + -21r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -21r + 20 + r2 = 0 + 20 Reorder the terms: -20 + 20 + -21r + r2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -21r + r2 = 0 + 20 -21r + r2 = 0 + 20 Combine like terms: 0 + 20 = 20 -21r + r2 = 20 The r term is -21r. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21r + 110.25 + r2 = 20 + 110.25 Reorder the terms: 110.25 + -21r + r2 = 20 + 110.25 Combine like terms: 20 + 110.25 = 130.25 110.25 + -21r + r2 = 130.25 Factor a perfect square on the left side: (r + -10.5)(r + -10.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (r + -10.5) equal to 11.412712211 and -11.412712211.Subproblem 1
r + -10.5 = 11.412712211 Simplifying r + -10.5 = 11.412712211 Reorder the terms: -10.5 + r = 11.412712211 Solving -10.5 + r = 11.412712211 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + r = 11.412712211 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + r = 11.412712211 + 10.5 r = 11.412712211 + 10.5 Combine like terms: 11.412712211 + 10.5 = 21.912712211 r = 21.912712211 Simplifying r = 21.912712211Subproblem 2
r + -10.5 = -11.412712211 Simplifying r + -10.5 = -11.412712211 Reorder the terms: -10.5 + r = -11.412712211 Solving -10.5 + r = -11.412712211 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + r = -11.412712211 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + r = -11.412712211 + 10.5 r = -11.412712211 + 10.5 Combine like terms: -11.412712211 + 10.5 = -0.912712211 r = -0.912712211 Simplifying r = -0.912712211Solution
The solution to the problem is based on the solutions from the subproblems. r = {21.912712211, -0.912712211}
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