x^2+11x+19=0

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Solution for x^2+11x+19=0 equation: 


Simplifying
x2 + 11x + 19 = 0

Reorder the terms:
19 + 11x + x2 = 0

Solving
19 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + 11x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + 11x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 11x + x2 = 0 + -19
11x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
11x + x2 = -19

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -19 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -19 + 30.25

Combine like terms: -19 + 30.25 = 11.25
30.25 + 11x + x2 = 11.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 5.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + 5.5 = 3.354101966

Simplifying
x + 5.5 = 3.354101966

Reorder the terms:
5.5 + x = 3.354101966

Solving
5.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 3.354101966 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 3.354101966 + -5.5
x = 3.354101966 + -5.5

Combine like terms: 3.354101966 + -5.5 = -2.145898034
x = -2.145898034

Simplifying
x = -2.145898034


Subproblem 2
x + 5.5 = -3.354101966

Simplifying
x + 5.5 = -3.354101966

Reorder the terms:
5.5 + x = -3.354101966

Solving
5.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -3.354101966 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -3.354101966 + -5.5
x = -3.354101966 + -5.5

Combine like terms: -3.354101966 + -5.5 = -8.854101966
x = -8.854101966

Simplifying
x = -8.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.145898034, -8.854101966}

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