n^2+18n+5=0

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Solution for n^2+18n+5=0 equation:


Simplifying
n2 + 18n + 5 = 0

Reorder the terms:
5 + 18n + n2 = 0

Solving
5 + 18n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 18n + -5 + n2 = 0 + -5

Reorder the terms:
5 + -5 + 18n + n2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 18n + n2 = 0 + -5
18n + n2 = 0 + -5

Combine like terms: 0 + -5 = -5
18n + n2 = -5

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 = -5 + 81

Reorder the terms:
81 + 18n + n2 = -5 + 81

Combine like terms: -5 + 81 = 76
81 + 18n + n2 = 76

Factor a perfect square on the left side:
(n + 9)(n + 9) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(n + 9) equal to 8.717797887 and -8.717797887.

Subproblem 1

n + 9 = 8.717797887 Simplifying n + 9 = 8.717797887 Reorder the terms: 9 + n = 8.717797887 Solving 9 + n = 8.717797887 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 = 8.717797887 + -9 Combine like terms: 9 + -9 = 0 0 + n = 8.717797887 + -9 n = 8.717797887 + -9 Combine like terms: 8.717797887 + -9 = -0.282202113 n = -0.282202113 Simplifying n = -0.282202113

Subproblem 2

n + 9 = -8.717797887 Simplifying n + 9 = -8.717797887 Reorder the terms: 9 + n = -8.717797887 Solving 9 + n = -8.717797887 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 = -8.717797887 + -9 Combine like terms: 9 + -9 = 0 0 + n = -8.717797887 + -9 n = -8.717797887 + -9 Combine like terms: -8.717797887 + -9 = -17.717797887 n = -17.717797887 Simplifying n = -17.717797887

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-0.282202113, -17.717797887}

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