x^2+0.0004384x-0.0002609=0

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Solution for x^2+0.0004384x-0.0002609=0 equation: 


Simplifying
x2 + 0.0004384x + -0.0002609 = 0

Reorder the terms:
-0.0002609 + 0.0004384x + x2 = 0

Solving
-0.0002609 + 0.0004384x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.0002609' to each side of the equation.
-0.0002609 + 0.0004384x + 0.0002609 + x2 = 0 + 0.0002609

Reorder the terms:
-0.0002609 + 0.0002609 + 0.0004384x + x2 = 0 + 0.0002609

Combine like terms: -0.0002609 + 0.0002609 = 0.0000000
0.0000000 + 0.0004384x + x2 = 0 + 0.0002609
0.0004384x + x2 = 0 + 0.0002609

Combine like terms: 0 + 0.0002609 = 0.0002609
0.0004384x + x2 = 0.0002609

The x term is 0.0004384x.  Take half its coefficient (0.0002192).
Square it (0.00000004804864) and add it to both sides.

Add '0.00000004804864' to each side of the equation.
0.0004384x + 0.00000004804864 + x2 = 0.0002609 + 0.00000004804864

Reorder the terms:
0.00000004804864 + 0.0004384x + x2 = 0.0002609 + 0.00000004804864

Combine like terms: 0.0002609 + 0.00000004804864 = 0.00026094804864
0.00000004804864 + 0.0004384x + x2 = 0.00026094804864

Factor a perfect square on the left side:
(x + 0.0002192)(x + 0.0002192) = 0.00026094804864

Calculate the square root of the right side: 0.016153886

Break this problem into two subproblems by setting 
(x + 0.0002192) equal to 0.016153886 and -0.016153886.


Subproblem 1
x + 0.0002192 = 0.016153886

Simplifying
x + 0.0002192 = 0.016153886

Reorder the terms:
0.0002192 + x = 0.016153886

Solving
0.0002192 + x = 0.016153886

Solving for variable 'x'.

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

Add '-0.0002192' to each side of the equation.
0.0002192 + -0.0002192 + x = 0.016153886 + -0.0002192

Combine like terms: 0.0002192 + -0.0002192 = 0.0000000
0.0000000 + x = 0.016153886 + -0.0002192
x = 0.016153886 + -0.0002192

Combine like terms: 0.016153886 + -0.0002192 = 0.015934686
x = 0.015934686

Simplifying
x = 0.015934686


Subproblem 2
x + 0.0002192 = -0.016153886

Simplifying
x + 0.0002192 = -0.016153886

Reorder the terms:
0.0002192 + x = -0.016153886

Solving
0.0002192 + x = -0.016153886

Solving for variable 'x'.

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

Add '-0.0002192' to each side of the equation.
0.0002192 + -0.0002192 + x = -0.016153886 + -0.0002192

Combine like terms: 0.0002192 + -0.0002192 = 0.0000000
0.0000000 + x = -0.016153886 + -0.0002192
x = -0.016153886 + -0.0002192

Combine like terms: -0.016153886 + -0.0002192 = -0.016373086
x = -0.016373086

Simplifying
x = -0.016373086


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.015934686, -0.016373086}

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