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Simplifying r2 = 9r + -1 Reorder the terms: r2 = -1 + 9r Solving r2 = -1 + 9r Solving for variable 'r'. Reorder the terms: 1 + -9r + r2 = -1 + 9r + 1 + -9r Reorder the terms: 1 + -9r + r2 = -1 + 1 + 9r + -9r Combine like terms: -1 + 1 = 0 1 + -9r + r2 = 0 + 9r + -9r 1 + -9r + r2 = 9r + -9r Combine like terms: 9r + -9r = 0 1 + -9r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -9r + -1 + r2 = 0 + -1 Reorder the terms: 1 + -1 + -9r + r2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9r + r2 = 0 + -1 -9r + r2 = 0 + -1 Combine like terms: 0 + -1 = -1 -9r + r2 = -1 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 = -1 + 20.25 Reorder the terms: 20.25 + -9r + r2 = -1 + 20.25 Combine like terms: -1 + 20.25 = 19.25 20.25 + -9r + r2 = 19.25 Factor a perfect square on the left side: (r + -4.5)(r + -4.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (r + -4.5) equal to 4.387482194 and -4.387482194.Subproblem 1
r + -4.5 = 4.387482194 Simplifying r + -4.5 = 4.387482194 Reorder the terms: -4.5 + r = 4.387482194 Solving -4.5 + r = 4.387482194 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 = 4.387482194 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = 4.387482194 + 4.5 r = 4.387482194 + 4.5 Combine like terms: 4.387482194 + 4.5 = 8.887482194 r = 8.887482194 Simplifying r = 8.887482194Subproblem 2
r + -4.5 = -4.387482194 Simplifying r + -4.5 = -4.387482194 Reorder the terms: -4.5 + r = -4.387482194 Solving -4.5 + r = -4.387482194 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 = -4.387482194 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = -4.387482194 + 4.5 r = -4.387482194 + 4.5 Combine like terms: -4.387482194 + 4.5 = 0.112517806 r = 0.112517806 Simplifying r = 0.112517806Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.887482194, 0.112517806}
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