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Simplifying r2 + -9r + 9 = 0 Reorder the terms: 9 + -9r + r2 = 0 Solving 9 + -9r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -9r + -9 + r2 = 0 + -9 Reorder the terms: 9 + -9 + -9r + r2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -9r + r2 = 0 + -9 -9r + r2 = 0 + -9 Combine like terms: 0 + -9 = -9 -9r + r2 = -9 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 = -9 + 20.25 Reorder the terms: 20.25 + -9r + r2 = -9 + 20.25 Combine like terms: -9 + 20.25 = 11.25 20.25 + -9r + r2 = 11.25 Factor a perfect square on the left side: (r + -4.5)(r + -4.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (r + -4.5) equal to 3.354101966 and -3.354101966.Subproblem 1
r + -4.5 = 3.354101966 Simplifying r + -4.5 = 3.354101966 Reorder the terms: -4.5 + r = 3.354101966 Solving -4.5 + r = 3.354101966 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 = 3.354101966 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = 3.354101966 + 4.5 r = 3.354101966 + 4.5 Combine like terms: 3.354101966 + 4.5 = 7.854101966 r = 7.854101966 Simplifying r = 7.854101966Subproblem 2
r + -4.5 = -3.354101966 Simplifying r + -4.5 = -3.354101966 Reorder the terms: -4.5 + r = -3.354101966 Solving -4.5 + r = -3.354101966 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 = -3.354101966 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = -3.354101966 + 4.5 r = -3.354101966 + 4.5 Combine like terms: -3.354101966 + 4.5 = 1.145898034 r = 1.145898034 Simplifying r = 1.145898034Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.854101966, 1.145898034}
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