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Simplifying n2 + 10n + -16 = 0 Reorder the terms: -16 + 10n + n2 = 0 Solving -16 + 10n + 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 + 10n + 16 + n2 = 0 + 16 Reorder the terms: -16 + 16 + 10n + n2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 10n + n2 = 0 + 16 10n + n2 = 0 + 16 Combine like terms: 0 + 16 = 16 10n + n2 = 16 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 = 16 + 25 Reorder the terms: 25 + 10n + n2 = 16 + 25 Combine like terms: 16 + 25 = 41 25 + 10n + n2 = 41 Factor a perfect square on the left side: (n + 5)(n + 5) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (n + 5) equal to 6.403124237 and -6.403124237.Subproblem 1
n + 5 = 6.403124237 Simplifying n + 5 = 6.403124237 Reorder the terms: 5 + n = 6.403124237 Solving 5 + n = 6.403124237 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 = 6.403124237 + -5 Combine like terms: 5 + -5 = 0 0 + n = 6.403124237 + -5 n = 6.403124237 + -5 Combine like terms: 6.403124237 + -5 = 1.403124237 n = 1.403124237 Simplifying n = 1.403124237Subproblem 2
n + 5 = -6.403124237 Simplifying n + 5 = -6.403124237 Reorder the terms: 5 + n = -6.403124237 Solving 5 + n = -6.403124237 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 = -6.403124237 + -5 Combine like terms: 5 + -5 = 0 0 + n = -6.403124237 + -5 n = -6.403124237 + -5 Combine like terms: -6.403124237 + -5 = -11.403124237 n = -11.403124237 Simplifying n = -11.403124237Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.403124237, -11.403124237}
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