1000000x^2+20x-4=0

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Solution for 1000000x^2+20x-4=0 equation: 


Simplifying
1000000x2 + 20x + -4 = 0

Reorder the terms:
-4 + 20x + 1000000x2 = 0

Solving
-4 + 20x + 1000000x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 5x + 250000x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 5x + 250000x2)' equal to zero and attempt to solve:

Simplifying
-1 + 5x + 250000x2 = 0

Solving
-1 + 5x + 250000x2 = 0

Begin completing the square.  Divide all terms by
250000 the coefficient of the squared term: 

Divide each side by '250000'.
-0.000004 + 0.00002x + x2 = 0.0000

Move the constant term to the right:

Add '0.000004' to each side of the equation.
-0.000004 + 0.00002x + 0.000004 + x2 = 0.0000 + 0.000004

Reorder the terms:
-0.000004 + 0.000004 + 0.00002x + x2 = 0.0000 + 0.000004

Combine like terms: -0.000004 + 0.000004 = 0.000000
0.000000 + 0.00002x + x2 = 0.0000 + 0.000004
0.00002x + x2 = 0.0000 + 0.000004

Combine like terms: 0.0000 + 0.000004 = 0.000004
0.00002x + x2 = 0.000004

The x term is 0.00002x.  Take half its coefficient (0.00001).
Square it (0.0000000001) and add it to both sides.

Add '0.0000000001' to each side of the equation.
0.00002x + 0.0000000001 + x2 = 0.000004 + 0.0000000001

Reorder the terms:
0.0000000001 + 0.00002x + x2 = 0.000004 + 0.0000000001

Combine like terms: 0.000004 + 0.0000000001 = 0.0000040001
0.0000000001 + 0.00002x + x2 = 0.0000040001

Factor a perfect square on the left side:
(x + 0.00001)(x + 0.00001) = 0.0000040001

Calculate the square root of the right side: 0.002000025

Break this problem into two subproblems by setting 
(x + 0.00001) equal to 0.002000025 and -0.002000025.


Subproblem 1
x + 0.00001 = 0.002000025

Simplifying
x + 0.00001 = 0.002000025

Reorder the terms:
0.00001 + x = 0.002000025

Solving
0.00001 + x = 0.002000025

Solving for variable 'x'.

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

Add '-0.00001' to each side of the equation.
0.00001 + -0.00001 + x = 0.002000025 + -0.00001

Combine like terms: 0.00001 + -0.00001 = 0.00000
0.00000 + x = 0.002000025 + -0.00001
x = 0.002000025 + -0.00001

Combine like terms: 0.002000025 + -0.00001 = 0.001990025
x = 0.001990025

Simplifying
x = 0.001990025


Subproblem 2
x + 0.00001 = -0.002000025

Simplifying
x + 0.00001 = -0.002000025

Reorder the terms:
0.00001 + x = -0.002000025

Solving
0.00001 + x = -0.002000025

Solving for variable 'x'.

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

Add '-0.00001' to each side of the equation.
0.00001 + -0.00001 + x = -0.002000025 + -0.00001

Combine like terms: 0.00001 + -0.00001 = 0.00000
0.00000 + x = -0.002000025 + -0.00001
x = -0.002000025 + -0.00001

Combine like terms: -0.002000025 + -0.00001 = -0.002010025
x = -0.002010025

Simplifying
x = -0.002010025


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.001990025, -0.002010025}
Solution
x = {0.001990025, -0.002010025}

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