x^2+27x+1=0

Solution for x^2+27x+1=0 equation:

Simplifying
x2 + 27x + 1 = 0

Reorder the terms:
1 + 27x + x2 = 0

Solving
1 + 27x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 27x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 27x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 27x + x2 = 0 + -1
27x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
27x + x2 = -1

The x term is 27x.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27x + 182.25 + x2 = -1 + 182.25

Reorder the terms:
182.25 + 27x + x2 = -1 + 182.25

Combine like terms: -1 + 182.25 = 181.25
182.25 + 27x + x2 = 181.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 181.25

Calculate the square root of the right side: 13.462912018

Break this problem into two subproblems by setting 
(x + 13.5) equal to 13.462912018 and -13.462912018.

Subproblem 1
x + 13.5 = 13.462912018

Simplifying
x + 13.5 = 13.462912018

Reorder the terms:
13.5 + x = 13.462912018

Solving
13.5 + x = 13.462912018

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = 13.462912018 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = 13.462912018 + -13.5
x = 13.462912018 + -13.5

Combine like terms: 13.462912018 + -13.5 = -0.037087982
x = -0.037087982

Simplifying
x = -0.037087982

Subproblem 2
x + 13.5 = -13.462912018

Simplifying
x + 13.5 = -13.462912018

Reorder the terms:
13.5 + x = -13.462912018

Solving
13.5 + x = -13.462912018

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = -13.462912018 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = -13.462912018 + -13.5
x = -13.462912018 + -13.5

Combine like terms: -13.462912018 + -13.5 = -26.962912018
x = -26.962912018

Simplifying
x = -26.962912018

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.037087982, -26.962912018}