500000000=1.36x^2+27.8x+304

Solution for 500000000=1.36x^2+27.8x+304 equation:

Simplifying
500000000 = 1.36x2 + 27.8x + 304

Reorder the terms:
500000000 = 304 + 27.8x + 1.36x2

Solving
500000000 = 304 + 27.8x + 1.36x2

Solving for variable 'x'.

Combine like terms: 500000000 + -304 = 499999696
499999696 + -27.8x + -1.36x2 = 304 + 27.8x + 1.36x2 + -304 + -27.8x + -1.36x2

Reorder the terms:
499999696 + -27.8x + -1.36x2 = 304 + -304 + 27.8x + -27.8x + 1.36x2 + -1.36x2

Combine like terms: 304 + -304 = 0
499999696 + -27.8x + -1.36x2 = 0 + 27.8x + -27.8x + 1.36x2 + -1.36x2
499999696 + -27.8x + -1.36x2 = 27.8x + -27.8x + 1.36x2 + -1.36x2

Combine like terms: 27.8x + -27.8x = 0.0
499999696 + -27.8x + -1.36x2 = 0.0 + 1.36x2 + -1.36x2
499999696 + -27.8x + -1.36x2 = 1.36x2 + -1.36x2

Combine like terms: 1.36x2 + -1.36x2 = 0.00
499999696 + -27.8x + -1.36x2 = 0.00

Begin completing the square.  Divide all terms by
-1.36 the coefficient of the squared term: 

Divide each side by '-1.36'.
-367646835.3 + 20.44117647x + x2 = 0

Move the constant term to the right:

Add '367646835.3' to each side of the equation.
-367646835.3 + 20.44117647x + 367646835.3 + x2 = 0 + 367646835.3

Reorder the terms:
-367646835.3 + 367646835.3 + 20.44117647x + x2 = 0 + 367646835.3

Combine like terms: -367646835.3 + 367646835.3 = 0.0
0.0 + 20.44117647x + x2 = 0 + 367646835.3
20.44117647x + x2 = 0 + 367646835.3

Combine like terms: 0 + 367646835.3 = 367646835.3
20.44117647x + x2 = 367646835.3

The x term is 20.44117647x.  Take half its coefficient (10.22058824).
Square it (104.4604240) and add it to both sides.

Add '104.4604240' to each side of the equation.
20.44117647x + 104.4604240 + x2 = 367646835.3 + 104.4604240

Reorder the terms:
104.4604240 + 20.44117647x + x2 = 367646835.3 + 104.4604240

Combine like terms: 367646835.3 + 104.4604240 = 367646939.760424
104.4604240 + 20.44117647x + x2 = 367646939.760424

Factor a perfect square on the left side:
(x + 10.22058824)(x + 10.22058824) = 367646939.760424

Calculate the square root of the right side: 19174.121616398

Break this problem into two subproblems by setting 
(x + 10.22058824) equal to 19174.121616398 and -19174.121616398.

Subproblem 1
x + 10.22058824 = 19174.121616398

Simplifying
x + 10.22058824 = 19174.121616398

Reorder the terms:
10.22058824 + x = 19174.121616398

Solving
10.22058824 + x = 19174.121616398

Solving for variable 'x'.

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

Add '-10.22058824' to each side of the equation.
10.22058824 + -10.22058824 + x = 19174.121616398 + -10.22058824

Combine like terms: 10.22058824 + -10.22058824 = 0.00000000
0.00000000 + x = 19174.121616398 + -10.22058824
x = 19174.121616398 + -10.22058824

Combine like terms: 19174.121616398 + -10.22058824 = 19163.901028158
x = 19163.901028158

Simplifying
x = 19163.901028158

Subproblem 2
x + 10.22058824 = -19174.121616398

Simplifying
x + 10.22058824 = -19174.121616398

Reorder the terms:
10.22058824 + x = -19174.121616398

Solving
10.22058824 + x = -19174.121616398

Solving for variable 'x'.

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

Add '-10.22058824' to each side of the equation.
10.22058824 + -10.22058824 + x = -19174.121616398 + -10.22058824

Combine like terms: 10.22058824 + -10.22058824 = 0.00000000
0.00000000 + x = -19174.121616398 + -10.22058824
x = -19174.121616398 + -10.22058824

Combine like terms: -19174.121616398 + -10.22058824 = -19184.342204638
x = -19184.342204638

Simplifying
x = -19184.342204638

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19163.901028158, -19184.342204638}