x^2+10x+19=0

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Solution for x^2+10x+19=0 equation: 


Simplifying
x2 + 10x + 19 = 0

Reorder the terms:
19 + 10x + x2 = 0

Solving
19 + 10x + 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 + 10x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + 10x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 10x + x2 = 0 + -19
10x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
10x + x2 = -19

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -19 + 25

Reorder the terms:
25 + 10x + x2 = -19 + 25

Combine like terms: -19 + 25 = 6
25 + 10x + x2 = 6

Factor a perfect square on the left side:
(x + 5)(x + 5) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + 5) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + 5 = 2.449489743

Simplifying
x + 5 = 2.449489743

Reorder the terms:
5 + x = 2.449489743

Solving
5 + x = 2.449489743

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 2.449489743 + -5

Combine like terms: 5 + -5 = 0
0 + x = 2.449489743 + -5
x = 2.449489743 + -5

Combine like terms: 2.449489743 + -5 = -2.550510257
x = -2.550510257

Simplifying
x = -2.550510257


Subproblem 2
x + 5 = -2.449489743

Simplifying
x + 5 = -2.449489743

Reorder the terms:
5 + x = -2.449489743

Solving
5 + x = -2.449489743

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -2.449489743 + -5

Combine like terms: 5 + -5 = 0
0 + x = -2.449489743 + -5
x = -2.449489743 + -5

Combine like terms: -2.449489743 + -5 = -7.449489743
x = -7.449489743

Simplifying
x = -7.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.550510257, -7.449489743}

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