X^2+.000018X-.0000045=0

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Solution for X^2+.000018X-.0000045=0 equation: 


Simplifying
X2 + 0.000018X + -0.0000045 = 0

Reorder the terms:
-0.0000045 + 0.000018X + X2 = 0

Solving
-0.0000045 + 0.000018X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '0.0000045' to each side of the equation.
-0.0000045 + 0.000018X + 0.0000045 + X2 = 0 + 0.0000045

Reorder the terms:
-0.0000045 + 0.0000045 + 0.000018X + X2 = 0 + 0.0000045

Combine like terms: -0.0000045 + 0.0000045 = 0.0000000
0.0000000 + 0.000018X + X2 = 0 + 0.0000045
0.000018X + X2 = 0 + 0.0000045

Combine like terms: 0 + 0.0000045 = 0.0000045
0.000018X + X2 = 0.0000045

The X term is 0.000018X.  Take half its coefficient (0.000009).
Square it (0.000000000081) and add it to both sides.

Add '0.000000000081' to each side of the equation.
0.000018X + 0.000000000081 + X2 = 0.0000045 + 0.000000000081

Reorder the terms:
0.000000000081 + 0.000018X + X2 = 0.0000045 + 0.000000000081

Combine like terms: 0.0000045 + 0.000000000081 = 0.000004500081
0.000000000081 + 0.000018X + X2 = 0.000004500081

Factor a perfect square on the left side:
(X + 0.000009)(X + 0.000009) = 0.000004500081

Calculate the square root of the right side: 0.002121339

Break this problem into two subproblems by setting 
(X + 0.000009) equal to 0.002121339 and -0.002121339.


Subproblem 1
X + 0.000009 = 0.002121339

Simplifying
X + 0.000009 = 0.002121339

Reorder the terms:
0.000009 + X = 0.002121339

Solving
0.000009 + X = 0.002121339

Solving for variable 'X'.

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

Add '-0.000009' to each side of the equation.
0.000009 + -0.000009 + X = 0.002121339 + -0.000009

Combine like terms: 0.000009 + -0.000009 = 0.000000
0.000000 + X = 0.002121339 + -0.000009
X = 0.002121339 + -0.000009

Combine like terms: 0.002121339 + -0.000009 = 0.002112339
X = 0.002112339

Simplifying
X = 0.002112339


Subproblem 2
X + 0.000009 = -0.002121339

Simplifying
X + 0.000009 = -0.002121339

Reorder the terms:
0.000009 + X = -0.002121339

Solving
0.000009 + X = -0.002121339

Solving for variable 'X'.

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

Add '-0.000009' to each side of the equation.
0.000009 + -0.000009 + X = -0.002121339 + -0.000009

Combine like terms: 0.000009 + -0.000009 = 0.000000
0.000000 + X = -0.002121339 + -0.000009
X = -0.002121339 + -0.000009

Combine like terms: -0.002121339 + -0.000009 = -0.002130339
X = -0.002130339

Simplifying
X = -0.002130339


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.002112339, -0.002130339}

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