X^2+0.001X-4=0

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Solution for X^2+0.001X-4=0 equation: 


Simplifying
X2 + 0.001X + -4 = 0

Reorder the terms:
-4 + 0.001X + X2 = 0

Solving
-4 + 0.001X + 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 + 0.001X + 4 + X2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.001X + X2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.001X + X2 = 0 + 4
0.001X + X2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.001X + X2 = 4

The X term is 0.001X.  Take half its coefficient (0.0005).
Square it (0.00000025) and add it to both sides.

Add '0.00000025' to each side of the equation.
0.001X + 0.00000025 + X2 = 4 + 0.00000025

Reorder the terms:
0.00000025 + 0.001X + X2 = 4 + 0.00000025

Combine like terms: 4 + 0.00000025 = 4.00000025
0.00000025 + 0.001X + X2 = 4.00000025

Factor a perfect square on the left side:
(X + 0.0005)(X + 0.0005) = 4.00000025

Calculate the square root of the right side: 2.000000063

Break this problem into two subproblems by setting 
(X + 0.0005) equal to 2.000000063 and -2.000000063.


Subproblem 1
X + 0.0005 = 2.000000063

Simplifying
X + 0.0005 = 2.000000063

Reorder the terms:
0.0005 + X = 2.000000063

Solving
0.0005 + X = 2.000000063

Solving for variable 'X'.

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

Add '-0.0005' to each side of the equation.
0.0005 + -0.0005 + X = 2.000000063 + -0.0005

Combine like terms: 0.0005 + -0.0005 = 0.0000
0.0000 + X = 2.000000063 + -0.0005
X = 2.000000063 + -0.0005

Combine like terms: 2.000000063 + -0.0005 = 1.999500063
X = 1.999500063

Simplifying
X = 1.999500063


Subproblem 2
X + 0.0005 = -2.000000063

Simplifying
X + 0.0005 = -2.000000063

Reorder the terms:
0.0005 + X = -2.000000063

Solving
0.0005 + X = -2.000000063

Solving for variable 'X'.

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

Add '-0.0005' to each side of the equation.
0.0005 + -0.0005 + X = -2.000000063 + -0.0005

Combine like terms: 0.0005 + -0.0005 = 0.0000
0.0000 + X = -2.000000063 + -0.0005
X = -2.000000063 + -0.0005

Combine like terms: -2.000000063 + -0.0005 = -2.000500063
X = -2.000500063

Simplifying
X = -2.000500063


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.999500063, -2.000500063}

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