10000x^2+2x-0.04=0

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Solution for 10000x^2+2x-0.04=0 equation: 


Simplifying
10000x2 + 2x + -0.04 = 0

Reorder the terms:
-0.04 + 2x + 10000x2 = 0

Solving
-0.04 + 2x + 10000x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
10000 the coefficient of the squared term: 

Divide each side by '10000'.
-0.000004 + 0.0002x + x2 = 0

Move the constant term to the right:

Add '0.000004' to each side of the equation.
-0.000004 + 0.0002x + 0.000004 + x2 = 0 + 0.000004

Reorder the terms:
-0.000004 + 0.000004 + 0.0002x + x2 = 0 + 0.000004

Combine like terms: -0.000004 + 0.000004 = 0.000000
0.000000 + 0.0002x + x2 = 0 + 0.000004
0.0002x + x2 = 0 + 0.000004

Combine like terms: 0 + 0.000004 = 0.000004
0.0002x + x2 = 0.000004

The x term is 0.0002x.  Take half its coefficient (0.0001).
Square it (0.00000001) and add it to both sides.

Add '0.00000001' to each side of the equation.
0.0002x + 0.00000001 + x2 = 0.000004 + 0.00000001

Reorder the terms:
0.00000001 + 0.0002x + x2 = 0.000004 + 0.00000001

Combine like terms: 0.000004 + 0.00000001 = 0.00000401
0.00000001 + 0.0002x + x2 = 0.00000401

Factor a perfect square on the left side:
(x + 0.0001)(x + 0.0001) = 0.00000401

Calculate the square root of the right side: 0.002002498

Break this problem into two subproblems by setting 
(x + 0.0001) equal to 0.002002498 and -0.002002498.


Subproblem 1
x + 0.0001 = 0.002002498

Simplifying
x + 0.0001 = 0.002002498

Reorder the terms:
0.0001 + x = 0.002002498

Solving
0.0001 + x = 0.002002498

Solving for variable 'x'.

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

Add '-0.0001' to each side of the equation.
0.0001 + -0.0001 + x = 0.002002498 + -0.0001

Combine like terms: 0.0001 + -0.0001 = 0.0000
0.0000 + x = 0.002002498 + -0.0001
x = 0.002002498 + -0.0001

Combine like terms: 0.002002498 + -0.0001 = 0.001902498
x = 0.001902498

Simplifying
x = 0.001902498


Subproblem 2
x + 0.0001 = -0.002002498

Simplifying
x + 0.0001 = -0.002002498

Reorder the terms:
0.0001 + x = -0.002002498

Solving
0.0001 + x = -0.002002498

Solving for variable 'x'.

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

Add '-0.0001' to each side of the equation.
0.0001 + -0.0001 + x = -0.002002498 + -0.0001

Combine like terms: 0.0001 + -0.0001 = 0.0000
0.0000 + x = -0.002002498 + -0.0001
x = -0.002002498 + -0.0001

Combine like terms: -0.002002498 + -0.0001 = -0.002102498
x = -0.002102498

Simplifying
x = -0.002102498


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.001902498, -0.002102498}

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