328000=2x^2+18x+308

Solution for 328000=2x^2+18x+308 equation:

Simplifying
328000 = 2x2 + 18x + 308

Reorder the terms:
328000 = 308 + 18x + 2x2

Solving
328000 = 308 + 18x + 2x2

Solving for variable 'x'.

Combine like terms: 328000 + -308 = 327692
327692 + -18x + -2x2 = 308 + 18x + 2x2 + -308 + -18x + -2x2

Reorder the terms:
327692 + -18x + -2x2 = 308 + -308 + 18x + -18x + 2x2 + -2x2

Combine like terms: 308 + -308 = 0
327692 + -18x + -2x2 = 0 + 18x + -18x + 2x2 + -2x2
327692 + -18x + -2x2 = 18x + -18x + 2x2 + -2x2

Combine like terms: 18x + -18x = 0
327692 + -18x + -2x2 = 0 + 2x2 + -2x2
327692 + -18x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
327692 + -18x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(163846 + -9x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(163846 + -9x + -1x2)' equal to zero and attempt to solve:

Simplifying
163846 + -9x + -1x2 = 0

Solving
163846 + -9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-163846 + 9x + x2 = 0

Move the constant term to the right:

Add '163846' to each side of the equation.
-163846 + 9x + 163846 + x2 = 0 + 163846

Reorder the terms:
-163846 + 163846 + 9x + x2 = 0 + 163846

Combine like terms: -163846 + 163846 = 0
0 + 9x + x2 = 0 + 163846
9x + x2 = 0 + 163846

Combine like terms: 0 + 163846 = 163846
9x + x2 = 163846

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 = 163846 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 163846 + 20.25

Combine like terms: 163846 + 20.25 = 163866.25
20.25 + 9x + x2 = 163866.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 163866.25

Calculate the square root of the right side: 404.803964902

Break this problem into two subproblems by setting 
(x + 4.5) equal to 404.803964902 and -404.803964902.

Subproblem 1
x + 4.5 = 404.803964902

Simplifying
x + 4.5 = 404.803964902

Reorder the terms:
4.5 + x = 404.803964902

Solving
4.5 + x = 404.803964902

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 = 404.803964902 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 404.803964902 + -4.5
x = 404.803964902 + -4.5

Combine like terms: 404.803964902 + -4.5 = 400.303964902
x = 400.303964902

Simplifying
x = 400.303964902

Subproblem 2
x + 4.5 = -404.803964902

Simplifying
x + 4.5 = -404.803964902

Reorder the terms:
4.5 + x = -404.803964902

Solving
4.5 + x = -404.803964902

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 = -404.803964902 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -404.803964902 + -4.5
x = -404.803964902 + -4.5

Combine like terms: -404.803964902 + -4.5 = -409.303964902
x = -409.303964902

Simplifying
x = -409.303964902

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {400.303964902, -409.303964902}
Solution
x = {400.303964902, -409.303964902}