x^2+0.0014x-0.00004242=0

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Solution for x^2+0.0014x-0.00004242=0 equation: 


Simplifying
x2 + 0.0014x + -0.00004242 = 0

Reorder the terms:
-0.00004242 + 0.0014x + x2 = 0

Solving
-0.00004242 + 0.0014x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.00004242' to each side of the equation.
-0.00004242 + 0.0014x + 0.00004242 + x2 = 0 + 0.00004242

Reorder the terms:
-0.00004242 + 0.00004242 + 0.0014x + x2 = 0 + 0.00004242

Combine like terms: -0.00004242 + 0.00004242 = 0.00000000
0.00000000 + 0.0014x + x2 = 0 + 0.00004242
0.0014x + x2 = 0 + 0.00004242

Combine like terms: 0 + 0.00004242 = 0.00004242
0.0014x + x2 = 0.00004242

The x term is 0.0014x.  Take half its coefficient (0.0007).
Square it (0.00000049) and add it to both sides.

Add '0.00000049' to each side of the equation.
0.0014x + 0.00000049 + x2 = 0.00004242 + 0.00000049

Reorder the terms:
0.00000049 + 0.0014x + x2 = 0.00004242 + 0.00000049

Combine like terms: 0.00004242 + 0.00000049 = 0.00004291
0.00000049 + 0.0014x + x2 = 0.00004291

Factor a perfect square on the left side:
(x + 0.0007)(x + 0.0007) = 0.00004291

Calculate the square root of the right side: 0.006550572

Break this problem into two subproblems by setting 
(x + 0.0007) equal to 0.006550572 and -0.006550572.


Subproblem 1
x + 0.0007 = 0.006550572

Simplifying
x + 0.0007 = 0.006550572

Reorder the terms:
0.0007 + x = 0.006550572

Solving
0.0007 + x = 0.006550572

Solving for variable 'x'.

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

Add '-0.0007' to each side of the equation.
0.0007 + -0.0007 + x = 0.006550572 + -0.0007

Combine like terms: 0.0007 + -0.0007 = 0.0000
0.0000 + x = 0.006550572 + -0.0007
x = 0.006550572 + -0.0007

Combine like terms: 0.006550572 + -0.0007 = 0.005850572
x = 0.005850572

Simplifying
x = 0.005850572


Subproblem 2
x + 0.0007 = -0.006550572

Simplifying
x + 0.0007 = -0.006550572

Reorder the terms:
0.0007 + x = -0.006550572

Solving
0.0007 + x = -0.006550572

Solving for variable 'x'.

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

Add '-0.0007' to each side of the equation.
0.0007 + -0.0007 + x = -0.006550572 + -0.0007

Combine like terms: 0.0007 + -0.0007 = 0.0000
0.0000 + x = -0.006550572 + -0.0007
x = -0.006550572 + -0.0007

Combine like terms: -0.006550572 + -0.0007 = -0.007250572
x = -0.007250572

Simplifying
x = -0.007250572


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.005850572, -0.007250572}

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