X^2+0.999X-0.001=0

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Solution for X^2+0.999X-0.001=0 equation: 


Simplifying
X2 + 0.999X + -0.001 = 0

Reorder the terms:
-0.001 + 0.999X + X2 = 0

Solving
-0.001 + 0.999X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '0.001' to each side of the equation.
-0.001 + 0.999X + 0.001 + X2 = 0 + 0.001

Reorder the terms:
-0.001 + 0.001 + 0.999X + X2 = 0 + 0.001

Combine like terms: -0.001 + 0.001 = 0.000
0.000 + 0.999X + X2 = 0 + 0.001
0.999X + X2 = 0 + 0.001

Combine like terms: 0 + 0.001 = 0.001
0.999X + X2 = 0.001

The X term is 0.999X.  Take half its coefficient (0.4995).
Square it (0.24950025) and add it to both sides.

Add '0.24950025' to each side of the equation.
0.999X + 0.24950025 + X2 = 0.001 + 0.24950025

Reorder the terms:
0.24950025 + 0.999X + X2 = 0.001 + 0.24950025

Combine like terms: 0.001 + 0.24950025 = 0.25050025
0.24950025 + 0.999X + X2 = 0.25050025

Factor a perfect square on the left side:
(X + 0.4995)(X + 0.4995) = 0.25050025

Calculate the square root of the right side: 0.5005

Break this problem into two subproblems by setting 
(X + 0.4995) equal to 0.5005 and -0.5005.


Subproblem 1
X + 0.4995 = 0.5005

Simplifying
X + 0.4995 = 0.5005

Reorder the terms:
0.4995 + X = 0.5005

Solving
0.4995 + X = 0.5005

Solving for variable 'X'.

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

Add '-0.4995' to each side of the equation.
0.4995 + -0.4995 + X = 0.5005 + -0.4995

Combine like terms: 0.4995 + -0.4995 = 0.0000
0.0000 + X = 0.5005 + -0.4995
X = 0.5005 + -0.4995

Combine like terms: 0.5005 + -0.4995 = 0.001
X = 0.001

Simplifying
X = 0.001


Subproblem 2
X + 0.4995 = -0.5005

Simplifying
X + 0.4995 = -0.5005

Reorder the terms:
0.4995 + X = -0.5005

Solving
0.4995 + X = -0.5005

Solving for variable 'X'.

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

Add '-0.4995' to each side of the equation.
0.4995 + -0.4995 + X = -0.5005 + -0.4995

Combine like terms: 0.4995 + -0.4995 = 0.0000
0.0000 + X = -0.5005 + -0.4995
X = -0.5005 + -0.4995

Combine like terms: -0.5005 + -0.4995 = -1
X = -1

Simplifying
X = -1


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.001, -1}

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