x^2-2001x+2500=0

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Solution for x^2-2001x+2500=0 equation: 


Simplifying
x2 + -2001x + 2500 = 0

Reorder the terms:
2500 + -2001x + x2 = 0

Solving
2500 + -2001x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2500' to each side of the equation.
2500 + -2001x + -2500 + x2 = 0 + -2500

Reorder the terms:
2500 + -2500 + -2001x + x2 = 0 + -2500

Combine like terms: 2500 + -2500 = 0
0 + -2001x + x2 = 0 + -2500
-2001x + x2 = 0 + -2500

Combine like terms: 0 + -2500 = -2500
-2001x + x2 = -2500

The x term is -2001x.  Take half its coefficient (-1000.5).
Square it (1001000.25) and add it to both sides.

Add '1001000.25' to each side of the equation.
-2001x + 1001000.25 + x2 = -2500 + 1001000.25

Reorder the terms:
1001000.25 + -2001x + x2 = -2500 + 1001000.25

Combine like terms: -2500 + 1001000.25 = 998500.25
1001000.25 + -2001x + x2 = 998500.25

Factor a perfect square on the left side:
(x + -1000.5)(x + -1000.5) = 998500.25

Calculate the square root of the right side: 999.249843633

Break this problem into two subproblems by setting 
(x + -1000.5) equal to 999.249843633 and -999.249843633.


Subproblem 1
x + -1000.5 = 999.249843633

Simplifying
x + -1000.5 = 999.249843633

Reorder the terms:
-1000.5 + x = 999.249843633

Solving
-1000.5 + x = 999.249843633

Solving for variable 'x'.

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

Add '1000.5' to each side of the equation.
-1000.5 + 1000.5 + x = 999.249843633 + 1000.5

Combine like terms: -1000.5 + 1000.5 = 0.0
0.0 + x = 999.249843633 + 1000.5
x = 999.249843633 + 1000.5

Combine like terms: 999.249843633 + 1000.5 = 1999.749843633
x = 1999.749843633

Simplifying
x = 1999.749843633


Subproblem 2
x + -1000.5 = -999.249843633

Simplifying
x + -1000.5 = -999.249843633

Reorder the terms:
-1000.5 + x = -999.249843633

Solving
-1000.5 + x = -999.249843633

Solving for variable 'x'.

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

Add '1000.5' to each side of the equation.
-1000.5 + 1000.5 + x = -999.249843633 + 1000.5

Combine like terms: -1000.5 + 1000.5 = 0.0
0.0 + x = -999.249843633 + 1000.5
x = -999.249843633 + 1000.5

Combine like terms: -999.249843633 + 1000.5 = 1.250156367
x = 1.250156367

Simplifying
x = 1.250156367


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1999.749843633, 1.250156367}

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