x^2-4000x+4=0

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Solution for x^2-4000x+4=0 equation: 


Simplifying
x2 + -4000x + 4 = 0

Reorder the terms:
4 + -4000x + x2 = 0

Solving
4 + -4000x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -4000x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -4000x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -4000x + x2 = 0 + -4
-4000x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-4000x + x2 = -4

The x term is -4000x.  Take half its coefficient (-2000).
Square it (4000000) and add it to both sides.

Add '4000000' to each side of the equation.
-4000x + 4000000 + x2 = -4 + 4000000

Reorder the terms:
4000000 + -4000x + x2 = -4 + 4000000

Combine like terms: -4 + 4000000 = 3999996
4000000 + -4000x + x2 = 3999996

Factor a perfect square on the left side:
(x + -2000)(x + -2000) = 3999996

Calculate the square root of the right side: 1999.999

Break this problem into two subproblems by setting 
(x + -2000) equal to 1999.999 and -1999.999.


Subproblem 1
x + -2000 = 1999.999

Simplifying
x + -2000 = 1999.999

Reorder the terms:
-2000 + x = 1999.999

Solving
-2000 + x = 1999.999

Solving for variable 'x'.

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

Add '2000' to each side of the equation.
-2000 + 2000 + x = 1999.999 + 2000

Combine like terms: -2000 + 2000 = 0
0 + x = 1999.999 + 2000
x = 1999.999 + 2000

Combine like terms: 1999.999 + 2000 = 3999.999
x = 3999.999

Simplifying
x = 3999.999


Subproblem 2
x + -2000 = -1999.999

Simplifying
x + -2000 = -1999.999

Reorder the terms:
-2000 + x = -1999.999

Solving
-2000 + x = -1999.999

Solving for variable 'x'.

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

Add '2000' to each side of the equation.
-2000 + 2000 + x = -1999.999 + 2000

Combine like terms: -2000 + 2000 = 0
0 + x = -1999.999 + 2000
x = -1999.999 + 2000

Combine like terms: -1999.999 + 2000 = 0.001
x = 0.001

Simplifying
x = 0.001


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3999.999, 0.001}

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