50=3.0804x^2+52.812x+227.05

Solution for 50=3.0804x^2+52.812x+227.05 equation:

Simplifying
50 = 3.0804x2 + 52.812x + 227.05

Reorder the terms:
50 = 227.05 + 52.812x + 3.0804x2

Solving
50 = 227.05 + 52.812x + 3.0804x2

Solving for variable 'x'.

Combine like terms: 50 + -227.05 = -177.05
-177.05 + -52.812x + -3.0804x2 = 227.05 + 52.812x + 3.0804x2 + -227.05 + -52.812x + -3.0804x2

Reorder the terms:
-177.05 + -52.812x + -3.0804x2 = 227.05 + -227.05 + 52.812x + -52.812x + 3.0804x2 + -3.0804x2

Combine like terms: 227.05 + -227.05 = 0.00
-177.05 + -52.812x + -3.0804x2 = 0.00 + 52.812x + -52.812x + 3.0804x2 + -3.0804x2
-177.05 + -52.812x + -3.0804x2 = 52.812x + -52.812x + 3.0804x2 + -3.0804x2

Combine like terms: 52.812x + -52.812x = 0.000
-177.05 + -52.812x + -3.0804x2 = 0.000 + 3.0804x2 + -3.0804x2
-177.05 + -52.812x + -3.0804x2 = 3.0804x2 + -3.0804x2

Combine like terms: 3.0804x2 + -3.0804x2 = 0.0000
-177.05 + -52.812x + -3.0804x2 = 0.0000

Begin completing the square.  Divide all terms by
-3.0804 the coefficient of the squared term: 

Divide each side by '-3.0804'.
57.47630178 + 17.14452668x + x2 = 0

Move the constant term to the right:

Add '-57.47630178' to each side of the equation.
57.47630178 + 17.14452668x + -57.47630178 + x2 = 0 + -57.47630178

Reorder the terms:
57.47630178 + -57.47630178 + 17.14452668x + x2 = 0 + -57.47630178

Combine like terms: 57.47630178 + -57.47630178 = 0.00000000
0.00000000 + 17.14452668x + x2 = 0 + -57.47630178
17.14452668x + x2 = 0 + -57.47630178

Combine like terms: 0 + -57.47630178 = -57.47630178
17.14452668x + x2 = -57.47630178

The x term is 17.14452668x.  Take half its coefficient (8.57226334).
Square it (73.48369877) and add it to both sides.

Add '73.48369877' to each side of the equation.
17.14452668x + 73.48369877 + x2 = -57.47630178 + 73.48369877

Reorder the terms:
73.48369877 + 17.14452668x + x2 = -57.47630178 + 73.48369877

Combine like terms: -57.47630178 + 73.48369877 = 16.00739699
73.48369877 + 17.14452668x + x2 = 16.00739699

Factor a perfect square on the left side:
(x + 8.57226334)(x + 8.57226334) = 16.00739699

Calculate the square root of the right side: 4.000924517

Break this problem into two subproblems by setting 
(x + 8.57226334) equal to 4.000924517 and -4.000924517.

Subproblem 1
x + 8.57226334 = 4.000924517

Simplifying
x + 8.57226334 = 4.000924517

Reorder the terms:
8.57226334 + x = 4.000924517

Solving
8.57226334 + x = 4.000924517

Solving for variable 'x'.

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

Add '-8.57226334' to each side of the equation.
8.57226334 + -8.57226334 + x = 4.000924517 + -8.57226334

Combine like terms: 8.57226334 + -8.57226334 = 0.00000000
0.00000000 + x = 4.000924517 + -8.57226334
x = 4.000924517 + -8.57226334

Combine like terms: 4.000924517 + -8.57226334 = -4.571338823
x = -4.571338823

Simplifying
x = -4.571338823

Subproblem 2
x + 8.57226334 = -4.000924517

Simplifying
x + 8.57226334 = -4.000924517

Reorder the terms:
8.57226334 + x = -4.000924517

Solving
8.57226334 + x = -4.000924517

Solving for variable 'x'.

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

Add '-8.57226334' to each side of the equation.
8.57226334 + -8.57226334 + x = -4.000924517 + -8.57226334

Combine like terms: 8.57226334 + -8.57226334 = 0.00000000
0.00000000 + x = -4.000924517 + -8.57226334
x = -4.000924517 + -8.57226334

Combine like terms: -4.000924517 + -8.57226334 = -12.573187857
x = -12.573187857

Simplifying
x = -12.573187857

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.571338823, -12.573187857}