((4x)(4x))-200x=1800

Solution for ((4x)(4x))-200x=1800 equation:

Simplifying
((4x)(4x)) + -200x = 1800

Remove parenthesis around (4x)
(4x(4x)) + -200x = 1800

Remove parenthesis around (4x)
(4x * 4x) + -200x = 1800

Reorder the terms for easier multiplication:
(4 * 4x * x) + -200x = 1800

Multiply 4 * 4
(16x * x) + -200x = 1800

Multiply x * x
(16x2) + -200x = 1800

Reorder the terms:
-200x + (16x2) = 1800

Solving
-200x + (16x2) = 1800

Solving for variable 'x'.

Reorder the terms:
-1800 + -200x + (16x2) = 1800 + -1800

Combine like terms: 1800 + -1800 = 0
-1800 + -200x + (16x2) = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-225 + -25x + (2x2)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-225 + -25x + (2x2))' equal to zero and attempt to solve:

Simplifying
-225 + -25x + (2x2) = 0

Solving
-225 + -25x + (2x2) = 0

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

Divide each side by '2'.
-112.5 + -12.5x + x2 = 0

Move the constant term to the right:

Add '112.5' to each side of the equation.
-112.5 + -12.5x + 112.5 + x2 = 0 + 112.5

Reorder the terms:
-112.5 + 112.5 + -12.5x + x2 = 0 + 112.5

Combine like terms: -112.5 + 112.5 = 0.0
0.0 + -12.5x + x2 = 0 + 112.5
-12.5x + x2 = 0 + 112.5

Combine like terms: 0 + 112.5 = 112.5
-12.5x + x2 = 112.5

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = 112.5 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = 112.5 + 39.0625

Combine like terms: 112.5 + 39.0625 = 151.5625
39.0625 + -12.5x + x2 = 151.5625

Factor a perfect square on the left side:
((x) + -6.25)((x) + -6.25) = 151.5625

Calculate the square root of the right side: 12.311072252

Break this problem into two subproblems by setting 
((x) + -6.25) equal to 12.311072252 and -12.311072252.

Subproblem 1
(x) + -6.25 = 12.311072252

Simplifying
(x) + -6.25 = 12.311072252
x + -6.25 = 12.311072252

Reorder the terms:
-6.25 + x = 12.311072252

Solving
-6.25 + x = 12.311072252

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 12.311072252 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 12.311072252 + 6.25
x = 12.311072252 + 6.25

Combine like terms: 12.311072252 + 6.25 = 18.561072252
x = 18.561072252

Simplifying
x = 18.561072252

Subproblem 2
(x) + -6.25 = -12.311072252

Simplifying
(x) + -6.25 = -12.311072252
x + -6.25 = -12.311072252

Reorder the terms:
-6.25 + x = -12.311072252

Solving
-6.25 + x = -12.311072252

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -12.311072252 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -12.311072252 + 6.25
x = -12.311072252 + 6.25

Combine like terms: -12.311072252 + 6.25 = -6.061072252
x = -6.061072252

Simplifying
x = -6.061072252

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.561072252, -6.061072252}
Solution
x = {18.561072252, -6.061072252}