x^2+27x+41=

Solution for x^2+27x+41= equation:

Simplifying
x2 + 27x + 41 = 0

Reorder the terms:
41 + 27x + x2 = 0

Solving
41 + 27x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-41' to each side of the equation.
41 + 27x + -41 + x2 = 0 + -41

Reorder the terms:
41 + -41 + 27x + x2 = 0 + -41

Combine like terms: 41 + -41 = 0
0 + 27x + x2 = 0 + -41
27x + x2 = 0 + -41

Combine like terms: 0 + -41 = -41
27x + x2 = -41

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 = -41 + 182.25

Reorder the terms:
182.25 + 27x + x2 = -41 + 182.25

Combine like terms: -41 + 182.25 = 141.25
182.25 + 27x + x2 = 141.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 141.25

Calculate the square root of the right side: 11.884864324

Break this problem into two subproblems by setting 
(x + 13.5) equal to 11.884864324 and -11.884864324.

Subproblem 1
x + 13.5 = 11.884864324

Simplifying
x + 13.5 = 11.884864324

Reorder the terms:
13.5 + x = 11.884864324

Solving
13.5 + x = 11.884864324

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 = 11.884864324 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = 11.884864324 + -13.5
x = 11.884864324 + -13.5

Combine like terms: 11.884864324 + -13.5 = -1.615135676
x = -1.615135676

Simplifying
x = -1.615135676

Subproblem 2
x + 13.5 = -11.884864324

Simplifying
x + 13.5 = -11.884864324

Reorder the terms:
13.5 + x = -11.884864324

Solving
13.5 + x = -11.884864324

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 = -11.884864324 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = -11.884864324 + -13.5
x = -11.884864324 + -13.5

Combine like terms: -11.884864324 + -13.5 = -25.384864324
x = -25.384864324

Simplifying
x = -25.384864324

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.615135676, -25.384864324}