4x^2=353904-8968.8x+50.5x^2

Solution for 4x^2=353904-8968.8x+50.5x^2 equation:

Simplifying
4x2 = 353904 + -8968.8x + 50.5x2

Solving
4x2 = 353904 + -8968.8x + 50.5x2

Solving for variable 'x'.

Reorder the terms:
-353904 + 8968.8x + 4x2 + -50.5x2 = 353904 + -8968.8x + 50.5x2 + -353904 + 8968.8x + -50.5x2

Combine like terms: 4x2 + -50.5x2 = -46.5x2
-353904 + 8968.8x + -46.5x2 = 353904 + -8968.8x + 50.5x2 + -353904 + 8968.8x + -50.5x2

Reorder the terms:
-353904 + 8968.8x + -46.5x2 = 353904 + -353904 + -8968.8x + 8968.8x + 50.5x2 + -50.5x2

Combine like terms: 353904 + -353904 = 0
-353904 + 8968.8x + -46.5x2 = 0 + -8968.8x + 8968.8x + 50.5x2 + -50.5x2
-353904 + 8968.8x + -46.5x2 = -8968.8x + 8968.8x + 50.5x2 + -50.5x2

Combine like terms: -8968.8x + 8968.8x = 0.0
-353904 + 8968.8x + -46.5x2 = 0.0 + 50.5x2 + -50.5x2
-353904 + 8968.8x + -46.5x2 = 50.5x2 + -50.5x2

Combine like terms: 50.5x2 + -50.5x2 = 0.0
-353904 + 8968.8x + -46.5x2 = 0.0

Begin completing the square.  Divide all terms by
-46.5 the coefficient of the squared term: 

Divide each side by '-46.5'.
7610.83871 + -192.8774194x + x2 = 0

Move the constant term to the right:

Add '-7610.83871' to each side of the equation.
7610.83871 + -192.8774194x + -7610.83871 + x2 = 0 + -7610.83871

Reorder the terms:
7610.83871 + -7610.83871 + -192.8774194x + x2 = 0 + -7610.83871

Combine like terms: 7610.83871 + -7610.83871 = 0.00000
0.00000 + -192.8774194x + x2 = 0 + -7610.83871
-192.8774194x + x2 = 0 + -7610.83871

Combine like terms: 0 + -7610.83871 = -7610.83871
-192.8774194x + x2 = -7610.83871

The x term is -192.8774194x.  Take half its coefficient (-96.4387097).
Square it (9300.424729) and add it to both sides.

Add '9300.424729' to each side of the equation.
-192.8774194x + 9300.424729 + x2 = -7610.83871 + 9300.424729

Reorder the terms:
9300.424729 + -192.8774194x + x2 = -7610.83871 + 9300.424729

Combine like terms: -7610.83871 + 9300.424729 = 1689.586019
9300.424729 + -192.8774194x + x2 = 1689.586019

Factor a perfect square on the left side:
(x + -96.4387097)(x + -96.4387097) = 1689.586019

Calculate the square root of the right side: 41.104574186

Break this problem into two subproblems by setting 
(x + -96.4387097) equal to 41.104574186 and -41.104574186.

Subproblem 1
x + -96.4387097 = 41.104574186

Simplifying
x + -96.4387097 = 41.104574186

Reorder the terms:
-96.4387097 + x = 41.104574186

Solving
-96.4387097 + x = 41.104574186

Solving for variable 'x'.

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

Add '96.4387097' to each side of the equation.
-96.4387097 + 96.4387097 + x = 41.104574186 + 96.4387097

Combine like terms: -96.4387097 + 96.4387097 = 0.0000000
0.0000000 + x = 41.104574186 + 96.4387097
x = 41.104574186 + 96.4387097

Combine like terms: 41.104574186 + 96.4387097 = 137.543283886
x = 137.543283886

Simplifying
x = 137.543283886

Subproblem 2
x + -96.4387097 = -41.104574186

Simplifying
x + -96.4387097 = -41.104574186

Reorder the terms:
-96.4387097 + x = -41.104574186

Solving
-96.4387097 + x = -41.104574186

Solving for variable 'x'.

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

Add '96.4387097' to each side of the equation.
-96.4387097 + 96.4387097 + x = -41.104574186 + 96.4387097

Combine like terms: -96.4387097 + 96.4387097 = 0.0000000
0.0000000 + x = -41.104574186 + 96.4387097
x = -41.104574186 + 96.4387097

Combine like terms: -41.104574186 + 96.4387097 = 55.334135514
x = 55.334135514

Simplifying
x = 55.334135514

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {137.543283886, 55.334135514}