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Simplifying n2 = n + 18 Reorder the terms: n2 = 18 + n Solving n2 = 18 + n Solving for variable 'n'. Reorder the terms: -18 + -1n + n2 = 18 + n + -18 + -1n Reorder the terms: -18 + -1n + n2 = 18 + -18 + n + -1n Combine like terms: 18 + -18 = 0 -18 + -1n + n2 = 0 + n + -1n -18 + -1n + n2 = n + -1n Combine like terms: n + -1n = 0 -18 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -1n + 18 + n2 = 0 + 18 Reorder the terms: -18 + 18 + -1n + n2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1n + n2 = 0 + 18 -1n + n2 = 0 + 18 Combine like terms: 0 + 18 = 18 -1n + n2 = 18 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 18 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 0.25 + -1n + n2 = 18.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (n + -0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
n + -0.5 = 4.272001873 Simplifying n + -0.5 = 4.272001873 Reorder the terms: -0.5 + n = 4.272001873 Solving -0.5 + n = 4.272001873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 4.272001873 + 0.5 n = 4.272001873 + 0.5 Combine like terms: 4.272001873 + 0.5 = 4.772001873 n = 4.772001873 Simplifying n = 4.772001873Subproblem 2
n + -0.5 = -4.272001873 Simplifying n + -0.5 = -4.272001873 Reorder the terms: -0.5 + n = -4.272001873 Solving -0.5 + n = -4.272001873 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -4.272001873 + 0.5 n = -4.272001873 + 0.5 Combine like terms: -4.272001873 + 0.5 = -3.772001873 n = -3.772001873 Simplifying n = -3.772001873Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.772001873, -3.772001873}
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