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Simplifying n2 + 10n + -32 = 9 Reorder the terms: -32 + 10n + n2 = 9 Solving -32 + 10n + n2 = 9 Solving for variable 'n'. Reorder the terms: -32 + -9 + 10n + n2 = 9 + -9 Combine like terms: -32 + -9 = -41 -41 + 10n + n2 = 9 + -9 Combine like terms: 9 + -9 = 0 -41 + 10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 10n + 41 + n2 = 0 + 41 Reorder the terms: -41 + 41 + 10n + n2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 10n + n2 = 0 + 41 10n + n2 = 0 + 41 Combine like terms: 0 + 41 = 41 10n + n2 = 41 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 = 41 + 25 Reorder the terms: 25 + 10n + n2 = 41 + 25 Combine like terms: 41 + 25 = 66 25 + 10n + n2 = 66 Factor a perfect square on the left side: (n + 5)(n + 5) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (n + 5) equal to 8.124038405 and -8.124038405.Subproblem 1
n + 5 = 8.124038405 Simplifying n + 5 = 8.124038405 Reorder the terms: 5 + n = 8.124038405 Solving 5 + n = 8.124038405 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 = 8.124038405 + -5 Combine like terms: 5 + -5 = 0 0 + n = 8.124038405 + -5 n = 8.124038405 + -5 Combine like terms: 8.124038405 + -5 = 3.124038405 n = 3.124038405 Simplifying n = 3.124038405Subproblem 2
n + 5 = -8.124038405 Simplifying n + 5 = -8.124038405 Reorder the terms: 5 + n = -8.124038405 Solving 5 + n = -8.124038405 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 = -8.124038405 + -5 Combine like terms: 5 + -5 = 0 0 + n = -8.124038405 + -5 n = -8.124038405 + -5 Combine like terms: -8.124038405 + -5 = -13.124038405 n = -13.124038405 Simplifying n = -13.124038405Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.124038405, -13.124038405}
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