x^2-123x+1=0

Solution for x^2-123x+1=0 equation:

Simplifying
x2 + -123x + 1 = 0

Reorder the terms:
1 + -123x + x2 = 0

Solving
1 + -123x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -123x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -123x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -123x + x2 = 0 + -1
-123x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-123x + x2 = -1

The x term is -123x.  Take half its coefficient (-61.5).
Square it (3782.25) and add it to both sides.

Add '3782.25' to each side of the equation.
-123x + 3782.25 + x2 = -1 + 3782.25

Reorder the terms:
3782.25 + -123x + x2 = -1 + 3782.25

Combine like terms: -1 + 3782.25 = 3781.25
3782.25 + -123x + x2 = 3781.25

Factor a perfect square on the left side:
(x + -61.5)(x + -61.5) = 3781.25

Calculate the square root of the right side: 61.491869381

Break this problem into two subproblems by setting 
(x + -61.5) equal to 61.491869381 and -61.491869381.

Subproblem 1
x + -61.5 = 61.491869381

Simplifying
x + -61.5 = 61.491869381

Reorder the terms:
-61.5 + x = 61.491869381

Solving
-61.5 + x = 61.491869381

Solving for variable 'x'.

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

Add '61.5' to each side of the equation.
-61.5 + 61.5 + x = 61.491869381 + 61.5

Combine like terms: -61.5 + 61.5 = 0.0
0.0 + x = 61.491869381 + 61.5
x = 61.491869381 + 61.5

Combine like terms: 61.491869381 + 61.5 = 122.991869381
x = 122.991869381

Simplifying
x = 122.991869381

Subproblem 2
x + -61.5 = -61.491869381

Simplifying
x + -61.5 = -61.491869381

Reorder the terms:
-61.5 + x = -61.491869381

Solving
-61.5 + x = -61.491869381

Solving for variable 'x'.

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

Add '61.5' to each side of the equation.
-61.5 + 61.5 + x = -61.491869381 + 61.5

Combine like terms: -61.5 + 61.5 = 0.0
0.0 + x = -61.491869381 + 61.5
x = -61.491869381 + 61.5

Combine like terms: -61.491869381 + 61.5 = 0.008130619
x = 0.008130619

Simplifying
x = 0.008130619

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {122.991869381, 0.008130619}