-39.671192x^2+x+443.432625675216=0

Solution for -39.671192x^2+x+443.432625675216=0 equation:

Simplifying
-39.671192x2 + x + 443.432625675216 = 0

Reorder the terms:
443.432625675216 + x + -39.671192x2 = 0

Solving
443.432625675216 + x + -39.671192x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-39.671192 the coefficient of the squared term: 

Divide each side by '-39.671192'.
-11.17769856 + -0.02520720829x + x2 = 0

Move the constant term to the right:

Add '11.17769856' to each side of the equation.
-11.17769856 + -0.02520720829x + 11.17769856 + x2 = 0 + 11.17769856

Reorder the terms:
-11.17769856 + 11.17769856 + -0.02520720829x + x2 = 0 + 11.17769856

Combine like terms: -11.17769856 + 11.17769856 = 0.00000000
0.00000000 + -0.02520720829x + x2 = 0 + 11.17769856
-0.02520720829x + x2 = 0 + 11.17769856

Combine like terms: 0 + 11.17769856 = 11.17769856
-0.02520720829x + x2 = 11.17769856

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.02520720829x + 0.25 + x2 = 11.17769856 + 0.25

Reorder the terms:
0.25 + -0.02520720829x + x2 = 11.17769856 + 0.25

Combine like terms: 11.17769856 + 0.25 = 11.42769856
0.25 + -0.02520720829x + x2 = 11.42769856

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 11.42769856

Calculate the square root of the right side: 3.380487917

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.380487917 and -3.380487917.

Subproblem 1
x + 0.5 = 3.380487917

Simplifying
x + 0.5 = 3.380487917

Reorder the terms:
0.5 + x = 3.380487917

Solving
0.5 + x = 3.380487917

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 3.380487917 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.380487917 + -0.5
x = 3.380487917 + -0.5

Combine like terms: 3.380487917 + -0.5 = 2.880487917
x = 2.880487917

Simplifying
x = 2.880487917

Subproblem 2
x + 0.5 = -3.380487917

Simplifying
x + 0.5 = -3.380487917

Reorder the terms:
0.5 + x = -3.380487917

Solving
0.5 + x = -3.380487917

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -3.380487917 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.380487917 + -0.5
x = -3.380487917 + -0.5

Combine like terms: -3.380487917 + -0.5 = -3.880487917
x = -3.880487917

Simplifying
x = -3.880487917

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.880487917, -3.880487917}