X^2+X-0.003=0

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Solution for X^2+X-0.003=0 equation: 


Simplifying
X2 + X + -0.003 = 0

Reorder the terms:
-0.003 + X + X2 = 0

Solving
-0.003 + X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '0.003' to each side of the equation.
-0.003 + X + 0.003 + X2 = 0 + 0.003

Reorder the terms:
-0.003 + 0.003 + X + X2 = 0 + 0.003

Combine like terms: -0.003 + 0.003 = 0.000
0.000 + X + X2 = 0 + 0.003
X + X2 = 0 + 0.003

Combine like terms: 0 + 0.003 = 0.003
X + X2 = 0.003

The X term is X.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
X + 0.25 + X2 = 0.003 + 0.25

Reorder the terms:
0.25 + X + X2 = 0.003 + 0.25

Combine like terms: 0.003 + 0.25 = 0.253
0.25 + X + X2 = 0.253

Factor a perfect square on the left side:
(X + 0.5)(X + 0.5) = 0.253

Calculate the square root of the right side: 0.502991054

Break this problem into two subproblems by setting 
(X + 0.5) equal to 0.502991054 and -0.502991054.


Subproblem 1
X + 0.5 = 0.502991054

Simplifying
X + 0.5 = 0.502991054

Reorder the terms:
0.5 + X = 0.502991054

Solving
0.5 + X = 0.502991054

Solving for variable 'X'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + X = 0.502991054 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + X = 0.502991054 + -0.5
X = 0.502991054 + -0.5

Combine like terms: 0.502991054 + -0.5 = 0.002991054
X = 0.002991054

Simplifying
X = 0.002991054


Subproblem 2
X + 0.5 = -0.502991054

Simplifying
X + 0.5 = -0.502991054

Reorder the terms:
0.5 + X = -0.502991054

Solving
0.5 + X = -0.502991054

Solving for variable 'X'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + X = -0.502991054 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + X = -0.502991054 + -0.5
X = -0.502991054 + -0.5

Combine like terms: -0.502991054 + -0.5 = -1.002991054
X = -1.002991054

Simplifying
X = -1.002991054


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.002991054, -1.002991054}

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