x^2+19x+11=0

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


Simplifying
x2 + 19x + 11 = 0

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

Solving
11 + 19x + 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 + 19x + -11 + x2 = 0 + -11

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

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

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

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = -11 + 90.25

Reorder the terms:
90.25 + 19x + x2 = -11 + 90.25

Combine like terms: -11 + 90.25 = 79.25
90.25 + 19x + x2 = 79.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 79.25

Calculate the square root of the right side: 8.902246907

Break this problem into two subproblems by setting 
(x + 9.5) equal to 8.902246907 and -8.902246907.


Subproblem 1
x + 9.5 = 8.902246907

Simplifying
x + 9.5 = 8.902246907

Reorder the terms:
9.5 + x = 8.902246907

Solving
9.5 + x = 8.902246907

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 8.902246907 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 8.902246907 + -9.5
x = 8.902246907 + -9.5

Combine like terms: 8.902246907 + -9.5 = -0.597753093
x = -0.597753093

Simplifying
x = -0.597753093


Subproblem 2
x + 9.5 = -8.902246907

Simplifying
x + 9.5 = -8.902246907

Reorder the terms:
9.5 + x = -8.902246907

Solving
9.5 + x = -8.902246907

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = -8.902246907 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -8.902246907 + -9.5
x = -8.902246907 + -9.5

Combine like terms: -8.902246907 + -9.5 = -18.402246907
x = -18.402246907

Simplifying
x = -18.402246907


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.597753093, -18.402246907}

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