x^2+40x+11=0

Solution for x^2+40x+11=0 equation:

Simplifying
x2 + 40x + 11 = 0

Reorder the terms:
11 + 40x + x2 = 0

Solving
11 + 40x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 40x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + 40x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 40x + x2 = 0 + -11
40x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
40x + x2 = -11

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = -11 + 400

Reorder the terms:
400 + 40x + x2 = -11 + 400

Combine like terms: -11 + 400 = 389
400 + 40x + x2 = 389

Factor a perfect square on the left side:
(x + 20)(x + 20) = 389

Calculate the square root of the right side: 19.723082923

Break this problem into two subproblems by setting 
(x + 20) equal to 19.723082923 and -19.723082923.

Subproblem 1
x + 20 = 19.723082923

Simplifying
x + 20 = 19.723082923

Reorder the terms:
20 + x = 19.723082923

Solving
20 + x = 19.723082923

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = 19.723082923 + -20

Combine like terms: 20 + -20 = 0
0 + x = 19.723082923 + -20
x = 19.723082923 + -20

Combine like terms: 19.723082923 + -20 = -0.276917077
x = -0.276917077

Simplifying
x = -0.276917077

Subproblem 2
x + 20 = -19.723082923

Simplifying
x + 20 = -19.723082923

Reorder the terms:
20 + x = -19.723082923

Solving
20 + x = -19.723082923

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = -19.723082923 + -20

Combine like terms: 20 + -20 = 0
0 + x = -19.723082923 + -20
x = -19.723082923 + -20

Combine like terms: -19.723082923 + -20 = -39.723082923
x = -39.723082923

Simplifying
x = -39.723082923

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.276917077, -39.723082923}