(x+19)(x+19)=2

Solution for (x+19)(x+19)=2 equation:

Simplifying
(x + 19)(x + 19) = 2

Reorder the terms:
(19 + x)(x + 19) = 2

Reorder the terms:
(19 + x)(19 + x) = 2

Multiply (19 + x) * (19 + x)
(19(19 + x) + x(19 + x)) = 2
((19 * 19 + x * 19) + x(19 + x)) = 2
((361 + 19x) + x(19 + x)) = 2
(361 + 19x + (19 * x + x * x)) = 2
(361 + 19x + (19x + x2)) = 2

Combine like terms: 19x + 19x = 38x
(361 + 38x + x2) = 2

Solving
361 + 38x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
361 + -2 + 38x + x2 = 2 + -2

Combine like terms: 361 + -2 = 359
359 + 38x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
359 + 38x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-359' to each side of the equation.
359 + 38x + -359 + x2 = 0 + -359

Reorder the terms:
359 + -359 + 38x + x2 = 0 + -359

Combine like terms: 359 + -359 = 0
0 + 38x + x2 = 0 + -359
38x + x2 = 0 + -359

Combine like terms: 0 + -359 = -359
38x + x2 = -359

The x term is 38x.  Take half its coefficient (19).
Square it (361) and add it to both sides.

Add '361' to each side of the equation.
38x + 361 + x2 = -359 + 361

Reorder the terms:
361 + 38x + x2 = -359 + 361

Combine like terms: -359 + 361 = 2
361 + 38x + x2 = 2

Factor a perfect square on the left side:
(x + 19)(x + 19) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + 19) equal to 1.414213562 and -1.414213562.

Subproblem 1
x + 19 = 1.414213562

Simplifying
x + 19 = 1.414213562

Reorder the terms:
19 + x = 1.414213562

Solving
19 + x = 1.414213562

Solving for variable 'x'.

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

Add '-19' to each side of the equation.
19 + -19 + x = 1.414213562 + -19

Combine like terms: 19 + -19 = 0
0 + x = 1.414213562 + -19
x = 1.414213562 + -19

Combine like terms: 1.414213562 + -19 = -17.585786438
x = -17.585786438

Simplifying
x = -17.585786438

Subproblem 2
x + 19 = -1.414213562

Simplifying
x + 19 = -1.414213562

Reorder the terms:
19 + x = -1.414213562

Solving
19 + x = -1.414213562

Solving for variable 'x'.

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

Add '-19' to each side of the equation.
19 + -19 + x = -1.414213562 + -19

Combine like terms: 19 + -19 = 0
0 + x = -1.414213562 + -19
x = -1.414213562 + -19

Combine like terms: -1.414213562 + -19 = -20.414213562
x = -20.414213562

Simplifying
x = -20.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-17.585786438, -20.414213562}