x^2-4000x-4000000=0

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Solution for x^2-4000x-4000000=0 equation: 


Simplifying
x2 + -4000x + -4000000 = 0

Reorder the terms:
-4000000 + -4000x + x2 = 0

Solving
-4000000 + -4000x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4000000' to each side of the equation.
-4000000 + -4000x + 4000000 + x2 = 0 + 4000000

Reorder the terms:
-4000000 + 4000000 + -4000x + x2 = 0 + 4000000

Combine like terms: -4000000 + 4000000 = 0
0 + -4000x + x2 = 0 + 4000000
-4000x + x2 = 0 + 4000000

Combine like terms: 0 + 4000000 = 4000000
-4000x + x2 = 4000000

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 = 4000000 + 4000000

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

Combine like terms: 4000000 + 4000000 = 8000000
4000000 + -4000x + x2 = 8000000

Factor a perfect square on the left side:
(x + -2000)(x + -2000) = 8000000

Calculate the square root of the right side: 2828.427124746

Break this problem into two subproblems by setting 
(x + -2000) equal to 2828.427124746 and -2828.427124746.


Subproblem 1
x + -2000 = 2828.427124746

Simplifying
x + -2000 = 2828.427124746

Reorder the terms:
-2000 + x = 2828.427124746

Solving
-2000 + x = 2828.427124746

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 = 2828.427124746 + 2000

Combine like terms: -2000 + 2000 = 0
0 + x = 2828.427124746 + 2000
x = 2828.427124746 + 2000

Combine like terms: 2828.427124746 + 2000 = 4828.427124746
x = 4828.427124746

Simplifying
x = 4828.427124746


Subproblem 2
x + -2000 = -2828.427124746

Simplifying
x + -2000 = -2828.427124746

Reorder the terms:
-2000 + x = -2828.427124746

Solving
-2000 + x = -2828.427124746

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 = -2828.427124746 + 2000

Combine like terms: -2000 + 2000 = 0
0 + x = -2828.427124746 + 2000
x = -2828.427124746 + 2000

Combine like terms: -2828.427124746 + 2000 = -828.427124746
x = -828.427124746

Simplifying
x = -828.427124746


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4828.427124746, -828.427124746}

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