(200x^2)-9000x-98938=0

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Solution for (200x^2)-9000x-98938=0 equation: 


Simplifying
(200x2) + -9000x + -98938 = 0

Reorder the terms:
-98938 + -9000x + (200x2) = 0

Solving
-98938 + -9000x + (200x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-49469 + -4500x + (100x2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-49469 + -4500x + (100x2))' equal to zero and attempt to solve:

Simplifying
-49469 + -4500x + (100x2) = 0

Solving
-49469 + -4500x + (100x2) = 0

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

Divide each side by '100'.
-494.69 + -45x + x2 = 0.00

Move the constant term to the right:

Add '494.69' to each side of the equation.
-494.69 + -45x + 494.69 + x2 = 0.00 + 494.69

Reorder the terms:
-494.69 + 494.69 + -45x + x2 = 0.00 + 494.69

Combine like terms: -494.69 + 494.69 = 0.00
0.00 + -45x + x2 = 0.00 + 494.69
-45x + x2 = 0.00 + 494.69

Combine like terms: 0.00 + 494.69 = 494.69
-45x + x2 = 494.69

The x term is -45x.  Take half its coefficient (-22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
-45x + 506.25 + x2 = 494.69 + 506.25

Reorder the terms:
506.25 + -45x + x2 = 494.69 + 506.25

Combine like terms: 494.69 + 506.25 = 1000.94
506.25 + -45x + x2 = 1000.94

Factor a perfect square on the left side:
((x) + -22.5)((x) + -22.5) = 1000.94

Calculate the square root of the right side: 31.637635816

Break this problem into two subproblems by setting 
((x) + -22.5) equal to 31.637635816 and -31.637635816.


Subproblem 1
(x) + -22.5 = 31.637635816

Simplifying
(x) + -22.5 = 31.637635816
x + -22.5 = 31.637635816

Reorder the terms:
-22.5 + x = 31.637635816

Solving
-22.5 + x = 31.637635816

Solving for variable 'x'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + x = 31.637635816 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = 31.637635816 + 22.5
x = 31.637635816 + 22.5

Combine like terms: 31.637635816 + 22.5 = 54.137635816
x = 54.137635816

Simplifying
x = 54.137635816


Subproblem 2
(x) + -22.5 = -31.637635816

Simplifying
(x) + -22.5 = -31.637635816
x + -22.5 = -31.637635816

Reorder the terms:
-22.5 + x = -31.637635816

Solving
-22.5 + x = -31.637635816

Solving for variable 'x'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + x = -31.637635816 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = -31.637635816 + 22.5
x = -31.637635816 + 22.5

Combine like terms: -31.637635816 + 22.5 = -9.137635816
x = -9.137635816

Simplifying
x = -9.137635816


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {54.137635816, -9.137635816}
Solution
x = {54.137635816, -9.137635816}

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