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Simplifying n2 = -9n + -2 Reorder the terms: n2 = -2 + -9n Solving n2 = -2 + -9n Solving for variable 'n'. Reorder the terms: 2 + 9n + n2 = -2 + -9n + 2 + 9n Reorder the terms: 2 + 9n + n2 = -2 + 2 + -9n + 9n Combine like terms: -2 + 2 = 0 2 + 9n + n2 = 0 + -9n + 9n 2 + 9n + n2 = -9n + 9n Combine like terms: -9n + 9n = 0 2 + 9n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 9n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + 9n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9n + n2 = 0 + -2 9n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 9n + n2 = -2 The n term is 9n. 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. 9n + 20.25 + n2 = -2 + 20.25 Reorder the terms: 20.25 + 9n + n2 = -2 + 20.25 Combine like terms: -2 + 20.25 = 18.25 20.25 + 9n + n2 = 18.25 Factor a perfect square on the left side: (n + 4.5)(n + 4.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (n + 4.5) equal to 4.272001873 and -4.272001873.Subproblem 1
n + 4.5 = 4.272001873 Simplifying n + 4.5 = 4.272001873 Reorder the terms: 4.5 + n = 4.272001873 Solving 4.5 + n = 4.272001873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + n = 4.272001873 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + n = 4.272001873 + -4.5 n = 4.272001873 + -4.5 Combine like terms: 4.272001873 + -4.5 = -0.227998127 n = -0.227998127 Simplifying n = -0.227998127Subproblem 2
n + 4.5 = -4.272001873 Simplifying n + 4.5 = -4.272001873 Reorder the terms: 4.5 + n = -4.272001873 Solving 4.5 + n = -4.272001873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + n = -4.272001873 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + n = -4.272001873 + -4.5 n = -4.272001873 + -4.5 Combine like terms: -4.272001873 + -4.5 = -8.772001873 n = -8.772001873 Simplifying n = -8.772001873Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.227998127, -8.772001873}
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