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Simplifying r2 = 20 + -9r Solving r2 = 20 + -9r Solving for variable 'r'. Reorder the terms: -20 + 9r + r2 = 20 + -9r + -20 + 9r Reorder the terms: -20 + 9r + r2 = 20 + -20 + -9r + 9r Combine like terms: 20 + -20 = 0 -20 + 9r + r2 = 0 + -9r + 9r -20 + 9r + r2 = -9r + 9r Combine like terms: -9r + 9r = 0 -20 + 9r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 9r + 20 + r2 = 0 + 20 Reorder the terms: -20 + 20 + 9r + r2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 9r + r2 = 0 + 20 9r + r2 = 0 + 20 Combine like terms: 0 + 20 = 20 9r + r2 = 20 The r term is 9r. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9r + 20.25 + r2 = 20 + 20.25 Reorder the terms: 20.25 + 9r + r2 = 20 + 20.25 Combine like terms: 20 + 20.25 = 40.25 20.25 + 9r + r2 = 40.25 Factor a perfect square on the left side: (r + 4.5)(r + 4.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (r + 4.5) equal to 6.34428877 and -6.34428877.Subproblem 1
r + 4.5 = 6.34428877 Simplifying r + 4.5 = 6.34428877 Reorder the terms: 4.5 + r = 6.34428877 Solving 4.5 + r = 6.34428877 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + r = 6.34428877 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + r = 6.34428877 + -4.5 r = 6.34428877 + -4.5 Combine like terms: 6.34428877 + -4.5 = 1.84428877 r = 1.84428877 Simplifying r = 1.84428877Subproblem 2
r + 4.5 = -6.34428877 Simplifying r + 4.5 = -6.34428877 Reorder the terms: 4.5 + r = -6.34428877 Solving 4.5 + r = -6.34428877 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + r = -6.34428877 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + r = -6.34428877 + -4.5 r = -6.34428877 + -4.5 Combine like terms: -6.34428877 + -4.5 = -10.84428877 r = -10.84428877 Simplifying r = -10.84428877Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.84428877, -10.84428877}
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