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Simplifying n2 + -10n + 22 = 0 Reorder the terms: 22 + -10n + n2 = 0 Solving 22 + -10n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -10n + -22 + n2 = 0 + -22 Reorder the terms: 22 + -22 + -10n + n2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -10n + n2 = 0 + -22 -10n + n2 = 0 + -22 Combine like terms: 0 + -22 = -22 -10n + n2 = -22 The n term is -10n. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10n + 25 + n2 = -22 + 25 Reorder the terms: 25 + -10n + n2 = -22 + 25 Combine like terms: -22 + 25 = 3 25 + -10n + n2 = 3 Factor a perfect square on the left side: (n + -5)(n + -5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (n + -5) equal to 1.732050808 and -1.732050808.Subproblem 1
n + -5 = 1.732050808 Simplifying n + -5 = 1.732050808 Reorder the terms: -5 + n = 1.732050808 Solving -5 + n = 1.732050808 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = 1.732050808 + 5 Combine like terms: -5 + 5 = 0 0 + n = 1.732050808 + 5 n = 1.732050808 + 5 Combine like terms: 1.732050808 + 5 = 6.732050808 n = 6.732050808 Simplifying n = 6.732050808Subproblem 2
n + -5 = -1.732050808 Simplifying n + -5 = -1.732050808 Reorder the terms: -5 + n = -1.732050808 Solving -5 + n = -1.732050808 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = -1.732050808 + 5 Combine like terms: -5 + 5 = 0 0 + n = -1.732050808 + 5 n = -1.732050808 + 5 Combine like terms: -1.732050808 + 5 = 3.267949192 n = 3.267949192 Simplifying n = 3.267949192Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.732050808, 3.267949192}
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