x(325+5x)=4000

Solution for x(325+5x)=4000 equation:

Simplifying
x(325 + 5x) = 4000
(325 * x + 5x * x) = 4000
(325x + 5x2) = 4000

Solving
325x + 5x2 = 4000

Solving for variable 'x'.

Reorder the terms:
-4000 + 325x + 5x2 = 4000 + -4000

Combine like terms: 4000 + -4000 = 0
-4000 + 325x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-800 + 65x + x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-800 + 65x + x2)' equal to zero and attempt to solve:

Simplifying
-800 + 65x + x2 = 0

Solving
-800 + 65x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '800' to each side of the equation.
-800 + 65x + 800 + x2 = 0 + 800

Reorder the terms:
-800 + 800 + 65x + x2 = 0 + 800

Combine like terms: -800 + 800 = 0
0 + 65x + x2 = 0 + 800
65x + x2 = 0 + 800

Combine like terms: 0 + 800 = 800
65x + x2 = 800

The x term is 65x.  Take half its coefficient (32.5).
Square it (1056.25) and add it to both sides.

Add '1056.25' to each side of the equation.
65x + 1056.25 + x2 = 800 + 1056.25

Reorder the terms:
1056.25 + 65x + x2 = 800 + 1056.25

Combine like terms: 800 + 1056.25 = 1856.25
1056.25 + 65x + x2 = 1856.25

Factor a perfect square on the left side:
(x + 32.5)(x + 32.5) = 1856.25

Calculate the square root of the right side: 43.084219849

Break this problem into two subproblems by setting 
(x + 32.5) equal to 43.084219849 and -43.084219849.

Subproblem 1
x + 32.5 = 43.084219849

Simplifying
x + 32.5 = 43.084219849

Reorder the terms:
32.5 + x = 43.084219849

Solving
32.5 + x = 43.084219849

Solving for variable 'x'.

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

Add '-32.5' to each side of the equation.
32.5 + -32.5 + x = 43.084219849 + -32.5

Combine like terms: 32.5 + -32.5 = 0.0
0.0 + x = 43.084219849 + -32.5
x = 43.084219849 + -32.5

Combine like terms: 43.084219849 + -32.5 = 10.584219849
x = 10.584219849

Simplifying
x = 10.584219849

Subproblem 2
x + 32.5 = -43.084219849

Simplifying
x + 32.5 = -43.084219849

Reorder the terms:
32.5 + x = -43.084219849

Solving
32.5 + x = -43.084219849

Solving for variable 'x'.

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

Add '-32.5' to each side of the equation.
32.5 + -32.5 + x = -43.084219849 + -32.5

Combine like terms: 32.5 + -32.5 = 0.0
0.0 + x = -43.084219849 + -32.5
x = -43.084219849 + -32.5

Combine like terms: -43.084219849 + -32.5 = -75.584219849
x = -75.584219849

Simplifying
x = -75.584219849

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.584219849, -75.584219849}
Solution
x = {10.584219849, -75.584219849}