3221.56997094199-185.827510129411x+-4952.45846835113x^2=0

Solution for 3221.56997094199-185.827510129411x+-4952.45846835113x^2=0 equation:

Simplifying
3221.56997094199 + -185.827510129411x + -4952.45846835113x2 = 0

Solving
3221.56997094199 + -185.827510129411x + -4952.45846835113x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4952.45846835113 the coefficient of the squared term: 

Divide each side by '-4952.45846835113'.
-0.6504991393 + 0.03752227531x + x2 = 0

Move the constant term to the right:

Add '0.6504991393' to each side of the equation.
-0.6504991393 + 0.03752227531x + 0.6504991393 + x2 = 0 + 0.6504991393

Reorder the terms:
-0.6504991393 + 0.6504991393 + 0.03752227531x + x2 = 0 + 0.6504991393

Combine like terms: -0.6504991393 + 0.6504991393 = 0.0000000000
0.0000000000 + 0.03752227531x + x2 = 0 + 0.6504991393
0.03752227531x + x2 = 0 + 0.6504991393

Combine like terms: 0 + 0.6504991393 = 0.6504991393
0.03752227531x + x2 = 0.6504991393

The x term is 0.03752227531x.  Take half its coefficient (0.01876113766).
Square it (0.0003519802863) and add it to both sides.

Add '0.0003519802863' to each side of the equation.
0.03752227531x + 0.0003519802863 + x2 = 0.6504991393 + 0.0003519802863

Reorder the terms:
0.0003519802863 + 0.03752227531x + x2 = 0.6504991393 + 0.0003519802863

Combine like terms: 0.6504991393 + 0.0003519802863 = 0.6508511195863
0.0003519802863 + 0.03752227531x + x2 = 0.6508511195863

Factor a perfect square on the left side:
(x + 0.01876113766)(x + 0.01876113766) = 0.6508511195863

Calculate the square root of the right side: 0.806753444

Break this problem into two subproblems by setting 
(x + 0.01876113766) equal to 0.806753444 and -0.806753444.

Subproblem 1
x + 0.01876113766 = 0.806753444

Simplifying
x + 0.01876113766 = 0.806753444

Reorder the terms:
0.01876113766 + x = 0.806753444

Solving
0.01876113766 + x = 0.806753444

Solving for variable 'x'.

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

Add '-0.01876113766' to each side of the equation.
0.01876113766 + -0.01876113766 + x = 0.806753444 + -0.01876113766

Combine like terms: 0.01876113766 + -0.01876113766 = 0.00000000000
0.00000000000 + x = 0.806753444 + -0.01876113766
x = 0.806753444 + -0.01876113766

Combine like terms: 0.806753444 + -0.01876113766 = 0.78799230634
x = 0.78799230634

Simplifying
x = 0.78799230634

Subproblem 2
x + 0.01876113766 = -0.806753444

Simplifying
x + 0.01876113766 = -0.806753444

Reorder the terms:
0.01876113766 + x = -0.806753444

Solving
0.01876113766 + x = -0.806753444

Solving for variable 'x'.

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

Add '-0.01876113766' to each side of the equation.
0.01876113766 + -0.01876113766 + x = -0.806753444 + -0.01876113766

Combine like terms: 0.01876113766 + -0.01876113766 = 0.00000000000
0.00000000000 + x = -0.806753444 + -0.01876113766
x = -0.806753444 + -0.01876113766

Combine like terms: -0.806753444 + -0.01876113766 = -0.82551458166
x = -0.82551458166

Simplifying
x = -0.82551458166

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.78799230634, -0.82551458166}