n^2+18n+15=0

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Solution for n^2+18n+15=0 equation:


Simplifying
n2 + 18n + 15 = 0

Reorder the terms:
15 + 18n + n2 = 0

Solving
15 + 18n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 18n + -15 + n2 = 0 + -15

Reorder the terms:
15 + -15 + 18n + n2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 18n + n2 = 0 + -15
18n + n2 = 0 + -15

Combine like terms: 0 + -15 = -15
18n + n2 = -15

The n term is 18n.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18n + 81 + n2 = -15 + 81

Reorder the terms:
81 + 18n + n2 = -15 + 81

Combine like terms: -15 + 81 = 66
81 + 18n + n2 = 66

Factor a perfect square on the left side:
(n + 9)(n + 9) = 66

Calculate the square root of the right side: 8.124038405

Break this problem into two subproblems by setting 
(n + 9) equal to 8.124038405 and -8.124038405.

Subproblem 1

n + 9 = 8.124038405 Simplifying n + 9 = 8.124038405 Reorder the terms: 9 + n = 8.124038405 Solving 9 + n = 8.124038405 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + n = 8.124038405 + -9 Combine like terms: 9 + -9 = 0 0 + n = 8.124038405 + -9 n = 8.124038405 + -9 Combine like terms: 8.124038405 + -9 = -0.875961595 n = -0.875961595 Simplifying n = -0.875961595

Subproblem 2

n + 9 = -8.124038405 Simplifying n + 9 = -8.124038405 Reorder the terms: 9 + n = -8.124038405 Solving 9 + n = -8.124038405 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + n = -8.124038405 + -9 Combine like terms: 9 + -9 = 0 0 + n = -8.124038405 + -9 n = -8.124038405 + -9 Combine like terms: -8.124038405 + -9 = -17.124038405 n = -17.124038405 Simplifying n = -17.124038405

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-0.875961595, -17.124038405}

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