x^2+27x+22=0

Solution for x^2+27x+22=0 equation:

Simplifying
x2 + 27x + 22 = 0

Reorder the terms:
22 + 27x + x2 = 0

Solving
22 + 27x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + 27x + -22 + x2 = 0 + -22

Reorder the terms:
22 + -22 + 27x + x2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 27x + x2 = 0 + -22
27x + x2 = 0 + -22

Combine like terms: 0 + -22 = -22
27x + x2 = -22

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 = -22 + 182.25

Reorder the terms:
182.25 + 27x + x2 = -22 + 182.25

Combine like terms: -22 + 182.25 = 160.25
182.25 + 27x + x2 = 160.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 160.25

Calculate the square root of the right side: 12.658988901

Break this problem into two subproblems by setting 
(x + 13.5) equal to 12.658988901 and -12.658988901.

Subproblem 1
x + 13.5 = 12.658988901

Simplifying
x + 13.5 = 12.658988901

Reorder the terms:
13.5 + x = 12.658988901

Solving
13.5 + x = 12.658988901

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 = 12.658988901 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = 12.658988901 + -13.5
x = 12.658988901 + -13.5

Combine like terms: 12.658988901 + -13.5 = -0.841011099
x = -0.841011099

Simplifying
x = -0.841011099

Subproblem 2
x + 13.5 = -12.658988901

Simplifying
x + 13.5 = -12.658988901

Reorder the terms:
13.5 + x = -12.658988901

Solving
13.5 + x = -12.658988901

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 = -12.658988901 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = -12.658988901 + -13.5
x = -12.658988901 + -13.5

Combine like terms: -12.658988901 + -13.5 = -26.158988901
x = -26.158988901

Simplifying
x = -26.158988901

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.841011099, -26.158988901}