2x(140+2x)=1800

Solution for 2x(140+2x)=1800 equation:

Simplifying
2x(140 + 2x) = 1800
(140 * 2x + 2x * 2x) = 1800
(280x + 4x2) = 1800

Solving
280x + 4x2 = 1800

Solving for variable 'x'.

Reorder the terms:
-1800 + 280x + 4x2 = 1800 + -1800

Combine like terms: 1800 + -1800 = 0
-1800 + 280x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-450 + 70x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-450 + 70x + x2)' equal to zero and attempt to solve:

Simplifying
-450 + 70x + x2 = 0

Solving
-450 + 70x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '450' to each side of the equation.
-450 + 70x + 450 + x2 = 0 + 450

Reorder the terms:
-450 + 450 + 70x + x2 = 0 + 450

Combine like terms: -450 + 450 = 0
0 + 70x + x2 = 0 + 450
70x + x2 = 0 + 450

Combine like terms: 0 + 450 = 450
70x + x2 = 450

The x term is 70x.  Take half its coefficient (35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
70x + 1225 + x2 = 450 + 1225

Reorder the terms:
1225 + 70x + x2 = 450 + 1225

Combine like terms: 450 + 1225 = 1675
1225 + 70x + x2 = 1675

Factor a perfect square on the left side:
(x + 35)(x + 35) = 1675

Calculate the square root of the right side: 40.926763859

Break this problem into two subproblems by setting 
(x + 35) equal to 40.926763859 and -40.926763859.

Subproblem 1
x + 35 = 40.926763859

Simplifying
x + 35 = 40.926763859

Reorder the terms:
35 + x = 40.926763859

Solving
35 + x = 40.926763859

Solving for variable 'x'.

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

Add '-35' to each side of the equation.
35 + -35 + x = 40.926763859 + -35

Combine like terms: 35 + -35 = 0
0 + x = 40.926763859 + -35
x = 40.926763859 + -35

Combine like terms: 40.926763859 + -35 = 5.926763859
x = 5.926763859

Simplifying
x = 5.926763859

Subproblem 2
x + 35 = -40.926763859

Simplifying
x + 35 = -40.926763859

Reorder the terms:
35 + x = -40.926763859

Solving
35 + x = -40.926763859

Solving for variable 'x'.

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

Add '-35' to each side of the equation.
35 + -35 + x = -40.926763859 + -35

Combine like terms: 35 + -35 = 0
0 + x = -40.926763859 + -35
x = -40.926763859 + -35

Combine like terms: -40.926763859 + -35 = -75.926763859
x = -75.926763859

Simplifying
x = -75.926763859

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.926763859, -75.926763859}
Solution
x = {5.926763859, -75.926763859}