-2000*x^2-1000*x-50=0

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Solution for -2000*x^2-1000*x-50=0 equation: 


Simplifying
-2000x2 + -1000x + -50 = 0

Reorder the terms:
-50 + -1000x + -2000x2 = 0

Solving
-50 + -1000x + -2000x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-50'.
-50(1 + 20x + 40x2) = 0

Ignore the factor -50.

Subproblem 1
Set the factor '(1 + 20x + 40x2)' equal to zero and attempt to solve:

Simplifying
1 + 20x + 40x2 = 0

Solving
1 + 20x + 40x2 = 0

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

Divide each side by '40'.
0.025 + 0.5x + x2 = 0.0

Move the constant term to the right:

Add '-0.025' to each side of the equation.
0.025 + 0.5x + -0.025 + x2 = 0.0 + -0.025

Reorder the terms:
0.025 + -0.025 + 0.5x + x2 = 0.0 + -0.025

Combine like terms: 0.025 + -0.025 = 0.000
0.000 + 0.5x + x2 = 0.0 + -0.025
0.5x + x2 = 0.0 + -0.025

Combine like terms: 0.0 + -0.025 = -0.025
0.5x + x2 = -0.025

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = -0.025 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -0.025 + 0.0625

Combine like terms: -0.025 + 0.0625 = 0.0375
0.0625 + 0.5x + x2 = 0.0375

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.0375

Calculate the square root of the right side: 0.193649167

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.193649167 and -0.193649167.


Subproblem 1
x + 0.25 = 0.193649167

Simplifying
x + 0.25 = 0.193649167

Reorder the terms:
0.25 + x = 0.193649167

Solving
0.25 + x = 0.193649167

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.193649167 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.193649167 + -0.25
x = 0.193649167 + -0.25

Combine like terms: 0.193649167 + -0.25 = -0.056350833
x = -0.056350833

Simplifying
x = -0.056350833


Subproblem 2
x + 0.25 = -0.193649167

Simplifying
x + 0.25 = -0.193649167

Reorder the terms:
0.25 + x = -0.193649167

Solving
0.25 + x = -0.193649167

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.193649167 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.193649167 + -0.25
x = -0.193649167 + -0.25

Combine like terms: -0.193649167 + -0.25 = -0.443649167
x = -0.443649167

Simplifying
x = -0.443649167


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.056350833, -0.443649167}
Solution
x = {-0.056350833, -0.443649167}

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