.0001x^2+.04x-2.1=0

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Solution for .0001x^2+.04x-2.1=0 equation: 


Simplifying
0.0001x2 + 0.04x + -2.1 = 0

Reorder the terms:
-2.1 + 0.04x + 0.0001x2 = 0

Solving
-2.1 + 0.04x + 0.0001x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.0001 the coefficient of the squared term: 

Divide each side by '0.0001'.
-21000 + 400x + x2 = 0

Move the constant term to the right:

Add '21000' to each side of the equation.
-21000 + 400x + 21000 + x2 = 0 + 21000

Reorder the terms:
-21000 + 21000 + 400x + x2 = 0 + 21000

Combine like terms: -21000 + 21000 = 0
0 + 400x + x2 = 0 + 21000
400x + x2 = 0 + 21000

Combine like terms: 0 + 21000 = 21000
400x + x2 = 21000

The x term is 400x.  Take half its coefficient (200).
Square it (40000) and add it to both sides.

Add '40000' to each side of the equation.
400x + 40000 + x2 = 21000 + 40000

Reorder the terms:
40000 + 400x + x2 = 21000 + 40000

Combine like terms: 21000 + 40000 = 61000
40000 + 400x + x2 = 61000

Factor a perfect square on the left side:
(x + 200)(x + 200) = 61000

Calculate the square root of the right side: 246.981780705

Break this problem into two subproblems by setting 
(x + 200) equal to 246.981780705 and -246.981780705.


Subproblem 1
x + 200 = 246.981780705

Simplifying
x + 200 = 246.981780705

Reorder the terms:
200 + x = 246.981780705

Solving
200 + x = 246.981780705

Solving for variable 'x'.

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

Add '-200' to each side of the equation.
200 + -200 + x = 246.981780705 + -200

Combine like terms: 200 + -200 = 0
0 + x = 246.981780705 + -200
x = 246.981780705 + -200

Combine like terms: 246.981780705 + -200 = 46.981780705
x = 46.981780705

Simplifying
x = 46.981780705


Subproblem 2
x + 200 = -246.981780705

Simplifying
x + 200 = -246.981780705

Reorder the terms:
200 + x = -246.981780705

Solving
200 + x = -246.981780705

Solving for variable 'x'.

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

Add '-200' to each side of the equation.
200 + -200 + x = -246.981780705 + -200

Combine like terms: 200 + -200 = 0
0 + x = -246.981780705 + -200
x = -246.981780705 + -200

Combine like terms: -246.981780705 + -200 = -446.981780705
x = -446.981780705

Simplifying
x = -446.981780705


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {46.981780705, -446.981780705}

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