38000=(9x-100)(11x-200)

Solution for 38000=(9x-100)(11x-200) equation:

Simplifying
38000 = (9x + -100)(11x + -200)

Reorder the terms:
38000 = (-100 + 9x)(11x + -200)

Reorder the terms:
38000 = (-100 + 9x)(-200 + 11x)

Multiply (-100 + 9x) * (-200 + 11x)
38000 = (-100(-200 + 11x) + 9x * (-200 + 11x))
38000 = ((-200 * -100 + 11x * -100) + 9x * (-200 + 11x))
38000 = ((20000 + -1100x) + 9x * (-200 + 11x))
38000 = (20000 + -1100x + (-200 * 9x + 11x * 9x))
38000 = (20000 + -1100x + (-1800x + 99x2))

Combine like terms: -1100x + -1800x = -2900x
38000 = (20000 + -2900x + 99x2)

Solving
38000 = 20000 + -2900x + 99x2

Solving for variable 'x'.

Combine like terms: 38000 + -20000 = 18000
18000 + 2900x + -99x2 = 20000 + -2900x + 99x2 + -20000 + 2900x + -99x2

Reorder the terms:
18000 + 2900x + -99x2 = 20000 + -20000 + -2900x + 2900x + 99x2 + -99x2

Combine like terms: 20000 + -20000 = 0
18000 + 2900x + -99x2 = 0 + -2900x + 2900x + 99x2 + -99x2
18000 + 2900x + -99x2 = -2900x + 2900x + 99x2 + -99x2

Combine like terms: -2900x + 2900x = 0
18000 + 2900x + -99x2 = 0 + 99x2 + -99x2
18000 + 2900x + -99x2 = 99x2 + -99x2

Combine like terms: 99x2 + -99x2 = 0
18000 + 2900x + -99x2 = 0

Begin completing the square.  Divide all terms by
-99 the coefficient of the squared term: 

Divide each side by '-99'.
-181.8181818 + -29.29292929x + x2 = 0

Move the constant term to the right:

Add '181.8181818' to each side of the equation.
-181.8181818 + -29.29292929x + 181.8181818 + x2 = 0 + 181.8181818

Reorder the terms:
-181.8181818 + 181.8181818 + -29.29292929x + x2 = 0 + 181.8181818

Combine like terms: -181.8181818 + 181.8181818 = 0.0000000
0.0000000 + -29.29292929x + x2 = 0 + 181.8181818
-29.29292929x + x2 = 0 + 181.8181818

Combine like terms: 0 + 181.8181818 = 181.8181818
-29.29292929x + x2 = 181.8181818

The x term is -29.29292929x.  Take half its coefficient (-14.64646465).
Square it (214.5189267) and add it to both sides.

Add '214.5189267' to each side of the equation.
-29.29292929x + 214.5189267 + x2 = 181.8181818 + 214.5189267

Reorder the terms:
214.5189267 + -29.29292929x + x2 = 181.8181818 + 214.5189267

Combine like terms: 181.8181818 + 214.5189267 = 396.3371085
214.5189267 + -29.29292929x + x2 = 396.3371085

Factor a perfect square on the left side:
(x + -14.64646465)(x + -14.64646465) = 396.3371085

Calculate the square root of the right side: 19.90821711

Break this problem into two subproblems by setting 
(x + -14.64646465) equal to 19.90821711 and -19.90821711.

Subproblem 1
x + -14.64646465 = 19.90821711

Simplifying
x + -14.64646465 = 19.90821711

Reorder the terms:
-14.64646465 + x = 19.90821711

Solving
-14.64646465 + x = 19.90821711

Solving for variable 'x'.

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

Add '14.64646465' to each side of the equation.
-14.64646465 + 14.64646465 + x = 19.90821711 + 14.64646465

Combine like terms: -14.64646465 + 14.64646465 = 0.00000000
0.00000000 + x = 19.90821711 + 14.64646465
x = 19.90821711 + 14.64646465

Combine like terms: 19.90821711 + 14.64646465 = 34.55468176
x = 34.55468176

Simplifying
x = 34.55468176

Subproblem 2
x + -14.64646465 = -19.90821711

Simplifying
x + -14.64646465 = -19.90821711

Reorder the terms:
-14.64646465 + x = -19.90821711

Solving
-14.64646465 + x = -19.90821711

Solving for variable 'x'.

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

Add '14.64646465' to each side of the equation.
-14.64646465 + 14.64646465 + x = -19.90821711 + 14.64646465

Combine like terms: -14.64646465 + 14.64646465 = 0.00000000
0.00000000 + x = -19.90821711 + 14.64646465
x = -19.90821711 + 14.64646465

Combine like terms: -19.90821711 + 14.64646465 = -5.26175246
x = -5.26175246

Simplifying
x = -5.26175246

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.55468176, -5.26175246}