x^2+0.000195x-0.000195=0

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Solution for x^2+0.000195x-0.000195=0 equation: 


Simplifying
x2 + 0.000195x + -0.000195 = 0

Reorder the terms:
-0.000195 + 0.000195x + x2 = 0

Solving
-0.000195 + 0.000195x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.000195' to each side of the equation.
-0.000195 + 0.000195x + 0.000195 + x2 = 0 + 0.000195

Reorder the terms:
-0.000195 + 0.000195 + 0.000195x + x2 = 0 + 0.000195

Combine like terms: -0.000195 + 0.000195 = 0.000000
0.000000 + 0.000195x + x2 = 0 + 0.000195
0.000195x + x2 = 0 + 0.000195

Combine like terms: 0 + 0.000195 = 0.000195
0.000195x + x2 = 0.000195

The x term is 0.000195x.  Take half its coefficient (0.0000975).
Square it (0.00000000950625) and add it to both sides.

Add '0.00000000950625' to each side of the equation.
0.000195x + 0.00000000950625 + x2 = 0.000195 + 0.00000000950625

Reorder the terms:
0.00000000950625 + 0.000195x + x2 = 0.000195 + 0.00000000950625

Combine like terms: 0.000195 + 0.00000000950625 = 0.00019500950625
0.00000000950625 + 0.000195x + x2 = 0.00019500950625

Factor a perfect square on the left side:
(x + 0.0000975)(x + 0.0000975) = 0.00019500950625

Calculate the square root of the right side: 0.01396458

Break this problem into two subproblems by setting 
(x + 0.0000975) equal to 0.01396458 and -0.01396458.


Subproblem 1
x + 0.0000975 = 0.01396458

Simplifying
x + 0.0000975 = 0.01396458

Reorder the terms:
0.0000975 + x = 0.01396458

Solving
0.0000975 + x = 0.01396458

Solving for variable 'x'.

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

Add '-0.0000975' to each side of the equation.
0.0000975 + -0.0000975 + x = 0.01396458 + -0.0000975

Combine like terms: 0.0000975 + -0.0000975 = 0.0000000
0.0000000 + x = 0.01396458 + -0.0000975
x = 0.01396458 + -0.0000975

Combine like terms: 0.01396458 + -0.0000975 = 0.01386708
x = 0.01386708

Simplifying
x = 0.01386708


Subproblem 2
x + 0.0000975 = -0.01396458

Simplifying
x + 0.0000975 = -0.01396458

Reorder the terms:
0.0000975 + x = -0.01396458

Solving
0.0000975 + x = -0.01396458

Solving for variable 'x'.

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

Add '-0.0000975' to each side of the equation.
0.0000975 + -0.0000975 + x = -0.01396458 + -0.0000975

Combine like terms: 0.0000975 + -0.0000975 = 0.0000000
0.0000000 + x = -0.01396458 + -0.0000975
x = -0.01396458 + -0.0000975

Combine like terms: -0.01396458 + -0.0000975 = -0.01406208
x = -0.01406208

Simplifying
x = -0.01406208


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.01386708, -0.01406208}

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