50x^2-450x-180000=0

Solution for 50x^2-450x-180000=0 equation:

Simplifying
50x2 + -450x + -180000 = 0

Reorder the terms:
-180000 + -450x + 50x2 = 0

Solving
-180000 + -450x + 50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '50'.
50(-3600 + -9x + x2) = 0

Ignore the factor 50.
Subproblem 1
Set the factor '(-3600 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
-3600 + -9x + x2 = 0

Solving
-3600 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3600' to each side of the equation.
-3600 + -9x + 3600 + x2 = 0 + 3600

Reorder the terms:
-3600 + 3600 + -9x + x2 = 0 + 3600

Combine like terms: -3600 + 3600 = 0
0 + -9x + x2 = 0 + 3600
-9x + x2 = 0 + 3600

Combine like terms: 0 + 3600 = 3600
-9x + x2 = 3600

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 3600 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 3600 + 20.25

Combine like terms: 3600 + 20.25 = 3620.25
20.25 + -9x + x2 = 3620.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 3620.25

Calculate the square root of the right side: 60.16851336

Break this problem into two subproblems by setting 
(x + -4.5) equal to 60.16851336 and -60.16851336.

Subproblem 1
x + -4.5 = 60.16851336

Simplifying
x + -4.5 = 60.16851336

Reorder the terms:
-4.5 + x = 60.16851336

Solving
-4.5 + x = 60.16851336

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 60.16851336 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 60.16851336 + 4.5
x = 60.16851336 + 4.5

Combine like terms: 60.16851336 + 4.5 = 64.66851336
x = 64.66851336

Simplifying
x = 64.66851336

Subproblem 2
x + -4.5 = -60.16851336

Simplifying
x + -4.5 = -60.16851336

Reorder the terms:
-4.5 + x = -60.16851336

Solving
-4.5 + x = -60.16851336

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -60.16851336 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -60.16851336 + 4.5
x = -60.16851336 + 4.5

Combine like terms: -60.16851336 + 4.5 = -55.66851336
x = -55.66851336

Simplifying
x = -55.66851336

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {64.66851336, -55.66851336}
Solution
x = {64.66851336, -55.66851336}