=x^2+19x+2

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

Simplifying
0 = x2 + 19x + 2

Reorder the terms:
0 = 2 + 19x + x2

Solving
0 = 2 + 19x + x2

Solving for variable 'x'.

Combine like terms: 0 + -2 = -2
-2 + -19x + -1x2 = 2 + 19x + x2 + -2 + -19x + -1x2

Reorder the terms:
-2 + -19x + -1x2 = 2 + -2 + 19x + -19x + x2 + -1x2

Combine like terms: 2 + -2 = 0
-2 + -19x + -1x2 = 0 + 19x + -19x + x2 + -1x2
-2 + -19x + -1x2 = 19x + -19x + x2 + -1x2

Combine like terms: 19x + -19x = 0
-2 + -19x + -1x2 = 0 + x2 + -1x2
-2 + -19x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + -19x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 19x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 19x + x2)' equal to zero and attempt to solve:

Simplifying
2 + 19x + x2 = 0

Solving
2 + 19x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 19x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 19x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 19x + x2 = 0 + -2
19x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
19x + x2 = -2

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 = -2 + 90.25

Reorder the terms:
90.25 + 19x + x2 = -2 + 90.25

Combine like terms: -2 + 90.25 = 88.25
90.25 + 19x + x2 = 88.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 88.25

Calculate the square root of the right side: 9.394147114

Break this problem into two subproblems by setting 
(x + 9.5) equal to 9.394147114 and -9.394147114.

Subproblem 1
x + 9.5 = 9.394147114

Simplifying
x + 9.5 = 9.394147114

Reorder the terms:
9.5 + x = 9.394147114

Solving
9.5 + x = 9.394147114

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 = 9.394147114 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 9.394147114 + -9.5
x = 9.394147114 + -9.5

Combine like terms: 9.394147114 + -9.5 = -0.105852886
x = -0.105852886

Simplifying
x = -0.105852886

Subproblem 2
x + 9.5 = -9.394147114

Simplifying
x + 9.5 = -9.394147114

Reorder the terms:
9.5 + x = -9.394147114

Solving
9.5 + x = -9.394147114

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 = -9.394147114 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -9.394147114 + -9.5
x = -9.394147114 + -9.5

Combine like terms: -9.394147114 + -9.5 = -18.894147114
x = -18.894147114

Simplifying
x = -18.894147114

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.105852886, -18.894147114}
Solution
x = {-0.105852886, -18.894147114}