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Simplifying n2 + -3n + -16 = 0 Reorder the terms: -16 + -3n + n2 = 0 Solving -16 + -3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -3n + 16 + n2 = 0 + 16 Reorder the terms: -16 + 16 + -3n + n2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -3n + n2 = 0 + 16 -3n + n2 = 0 + 16 Combine like terms: 0 + 16 = 16 -3n + n2 = 16 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 16 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 16 + 2.25 Combine like terms: 16 + 2.25 = 18.25 2.25 + -3n + n2 = 18.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (n + -1.5) equal to 4.272001873 and -4.272001873.Subproblem 1
n + -1.5 = 4.272001873 Simplifying n + -1.5 = 4.272001873 Reorder the terms: -1.5 + n = 4.272001873 Solving -1.5 + n = 4.272001873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 4.272001873 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 4.272001873 + 1.5 n = 4.272001873 + 1.5 Combine like terms: 4.272001873 + 1.5 = 5.772001873 n = 5.772001873 Simplifying n = 5.772001873Subproblem 2
n + -1.5 = -4.272001873 Simplifying n + -1.5 = -4.272001873 Reorder the terms: -1.5 + n = -4.272001873 Solving -1.5 + n = -4.272001873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -4.272001873 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -4.272001873 + 1.5 n = -4.272001873 + 1.5 Combine like terms: -4.272001873 + 1.5 = -2.772001873 n = -2.772001873 Simplifying n = -2.772001873Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.772001873, -2.772001873}
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