2x^2-1000x-80000=0

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Solution for 2x^2-1000x-80000=0 equation: 


Simplifying
2x2 + -1000x + -80000 = 0

Reorder the terms:
-80000 + -1000x + 2x2 = 0

Solving
-80000 + -1000x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-40000 + -500x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-40000 + -500x + x2)' equal to zero and attempt to solve:

Simplifying
-40000 + -500x + x2 = 0

Solving
-40000 + -500x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40000' to each side of the equation.
-40000 + -500x + 40000 + x2 = 0 + 40000

Reorder the terms:
-40000 + 40000 + -500x + x2 = 0 + 40000

Combine like terms: -40000 + 40000 = 0
0 + -500x + x2 = 0 + 40000
-500x + x2 = 0 + 40000

Combine like terms: 0 + 40000 = 40000
-500x + x2 = 40000

The x term is -500x.  Take half its coefficient (-250).
Square it (62500) and add it to both sides.

Add '62500' to each side of the equation.
-500x + 62500 + x2 = 40000 + 62500

Reorder the terms:
62500 + -500x + x2 = 40000 + 62500

Combine like terms: 40000 + 62500 = 102500
62500 + -500x + x2 = 102500

Factor a perfect square on the left side:
(x + -250)(x + -250) = 102500

Calculate the square root of the right side: 320.156211872

Break this problem into two subproblems by setting 
(x + -250) equal to 320.156211872 and -320.156211872.


Subproblem 1
x + -250 = 320.156211872

Simplifying
x + -250 = 320.156211872

Reorder the terms:
-250 + x = 320.156211872

Solving
-250 + x = 320.156211872

Solving for variable 'x'.

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

Add '250' to each side of the equation.
-250 + 250 + x = 320.156211872 + 250

Combine like terms: -250 + 250 = 0
0 + x = 320.156211872 + 250
x = 320.156211872 + 250

Combine like terms: 320.156211872 + 250 = 570.156211872
x = 570.156211872

Simplifying
x = 570.156211872


Subproblem 2
x + -250 = -320.156211872

Simplifying
x + -250 = -320.156211872

Reorder the terms:
-250 + x = -320.156211872

Solving
-250 + x = -320.156211872

Solving for variable 'x'.

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

Add '250' to each side of the equation.
-250 + 250 + x = -320.156211872 + 250

Combine like terms: -250 + 250 = 0
0 + x = -320.156211872 + 250
x = -320.156211872 + 250

Combine like terms: -320.156211872 + 250 = -70.156211872
x = -70.156211872

Simplifying
x = -70.156211872


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {570.156211872, -70.156211872}
Solution
x = {570.156211872, -70.156211872}

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