0.000084x^2-1.0000672x+0.00001344=0

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Solution for 0.000084x^2-1.0000672x+0.00001344=0 equation: 


Simplifying
0.000084x2 + -1.0000672x + 0.00001344 = 0

Reorder the terms:
0.00001344 + -1.0000672x + 0.000084x2 = 0

Solving
0.00001344 + -1.0000672x + 0.000084x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.000084 the coefficient of the squared term: 

Divide each side by '0.000084'.
0.16 + -11905.5619x + x2 = 0

Move the constant term to the right:

Add '-0.16' to each side of the equation.
0.16 + -11905.5619x + -0.16 + x2 = 0 + -0.16

Reorder the terms:
0.16 + -0.16 + -11905.5619x + x2 = 0 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + -11905.5619x + x2 = 0 + -0.16
-11905.5619x + x2 = 0 + -0.16

Combine like terms: 0 + -0.16 = -0.16
-11905.5619x + x2 = -0.16

The x term is -11905.5619x.  Take half its coefficient (-5952.78095).
Square it (35435601.04) and add it to both sides.

Add '35435601.04' to each side of the equation.
-11905.5619x + 35435601.04 + x2 = -0.16 + 35435601.04

Reorder the terms:
35435601.04 + -11905.5619x + x2 = -0.16 + 35435601.04

Combine like terms: -0.16 + 35435601.04 = 35435600.88
35435601.04 + -11905.5619x + x2 = 35435600.88

Factor a perfect square on the left side:
(x + -5952.78095)(x + -5952.78095) = 35435600.88

Calculate the square root of the right side: 5952.780936672

Break this problem into two subproblems by setting 
(x + -5952.78095) equal to 5952.780936672 and -5952.780936672.


Subproblem 1
x + -5952.78095 = 5952.780936672

Simplifying
x + -5952.78095 = 5952.780936672

Reorder the terms:
-5952.78095 + x = 5952.780936672

Solving
-5952.78095 + x = 5952.780936672

Solving for variable 'x'.

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

Add '5952.78095' to each side of the equation.
-5952.78095 + 5952.78095 + x = 5952.780936672 + 5952.78095

Combine like terms: -5952.78095 + 5952.78095 = 0.00000
0.00000 + x = 5952.780936672 + 5952.78095
x = 5952.780936672 + 5952.78095

Combine like terms: 5952.780936672 + 5952.78095 = 11905.561886672
x = 11905.561886672

Simplifying
x = 11905.561886672


Subproblem 2
x + -5952.78095 = -5952.780936672

Simplifying
x + -5952.78095 = -5952.780936672

Reorder the terms:
-5952.78095 + x = -5952.780936672

Solving
-5952.78095 + x = -5952.780936672

Solving for variable 'x'.

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

Add '5952.78095' to each side of the equation.
-5952.78095 + 5952.78095 + x = -5952.780936672 + 5952.78095

Combine like terms: -5952.78095 + 5952.78095 = 0.00000
0.00000 + x = -5952.780936672 + 5952.78095
x = -5952.780936672 + 5952.78095

Combine like terms: -5952.780936672 + 5952.78095 = 0.000013328
x = 0.000013328

Simplifying
x = 0.000013328


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11905.561886672, 0.000013328}

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