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Simplifying n2 + 10n + 24 = 2 Reorder the terms: 24 + 10n + n2 = 2 Solving 24 + 10n + n2 = 2 Solving for variable 'n'. Reorder the terms: 24 + -2 + 10n + n2 = 2 + -2 Combine like terms: 24 + -2 = 22 22 + 10n + n2 = 2 + -2 Combine like terms: 2 + -2 = 0 22 + 10n + n2 = 0 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 = -3.267949192 n = -3.267949192 Simplifying n = -3.267949192Subproblem 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 = -6.732050808 n = -6.732050808 Simplifying n = -6.732050808Solution
The solution to the problem is based on the solutions from the subproblems. n = {-3.267949192, -6.732050808}
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