3221.56997094199+181.186790357651x+-209.053188905878x^2=0

Solution for 3221.56997094199+181.186790357651x+-209.053188905878x^2=0 equation:

Simplifying
3221.56997094199 + 181.186790357651x + -209.053188905878x2 = 0

Solving
3221.56997094199 + 181.186790357651x + -209.053188905878x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-209.053188905878 the coefficient of the squared term: 

Divide each side by '-209.053188905878'.
-15.41028859 + -0.8667018729x + x2 = 0

Move the constant term to the right:

Add '15.41028859' to each side of the equation.
-15.41028859 + -0.8667018729x + 15.41028859 + x2 = 0 + 15.41028859

Reorder the terms:
-15.41028859 + 15.41028859 + -0.8667018729x + x2 = 0 + 15.41028859

Combine like terms: -15.41028859 + 15.41028859 = 0.00000000
0.00000000 + -0.8667018729x + x2 = 0 + 15.41028859
-0.8667018729x + x2 = 0 + 15.41028859

Combine like terms: 0 + 15.41028859 = 15.41028859
-0.8667018729x + x2 = 15.41028859

The x term is -0.8667018729x.  Take half its coefficient (-0.4333509365).
Square it (0.1877930342) and add it to both sides.

Add '0.1877930342' to each side of the equation.
-0.8667018729x + 0.1877930342 + x2 = 15.41028859 + 0.1877930342

Reorder the terms:
0.1877930342 + -0.8667018729x + x2 = 15.41028859 + 0.1877930342

Combine like terms: 15.41028859 + 0.1877930342 = 15.5980816242
0.1877930342 + -0.8667018729x + x2 = 15.5980816242

Factor a perfect square on the left side:
(x + -0.4333509365)(x + -0.4333509365) = 15.5980816242

Calculate the square root of the right side: 3.949440672

Break this problem into two subproblems by setting 
(x + -0.4333509365) equal to 3.949440672 and -3.949440672.

Subproblem 1
x + -0.4333509365 = 3.949440672

Simplifying
x + -0.4333509365 = 3.949440672

Reorder the terms:
-0.4333509365 + x = 3.949440672

Solving
-0.4333509365 + x = 3.949440672

Solving for variable 'x'.

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

Add '0.4333509365' to each side of the equation.
-0.4333509365 + 0.4333509365 + x = 3.949440672 + 0.4333509365

Combine like terms: -0.4333509365 + 0.4333509365 = 0.0000000000
0.0000000000 + x = 3.949440672 + 0.4333509365
x = 3.949440672 + 0.4333509365

Combine like terms: 3.949440672 + 0.4333509365 = 4.3827916085
x = 4.3827916085

Simplifying
x = 4.3827916085

Subproblem 2
x + -0.4333509365 = -3.949440672

Simplifying
x + -0.4333509365 = -3.949440672

Reorder the terms:
-0.4333509365 + x = -3.949440672

Solving
-0.4333509365 + x = -3.949440672

Solving for variable 'x'.

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

Add '0.4333509365' to each side of the equation.
-0.4333509365 + 0.4333509365 + x = -3.949440672 + 0.4333509365

Combine like terms: -0.4333509365 + 0.4333509365 = 0.0000000000
0.0000000000 + x = -3.949440672 + 0.4333509365
x = -3.949440672 + 0.4333509365

Combine like terms: -3.949440672 + 0.4333509365 = -3.5160897355
x = -3.5160897355

Simplifying
x = -3.5160897355

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.3827916085, -3.5160897355}