2(x^2)=2704-110x+4(x^2)-110x

Solution for 2(x^2)=2704-110x+4(x^2)-110x equation:

Simplifying
2(x2) = 2704 + -110x + 4(x2) + -110x

Reorder the terms:
2x2 = 2704 + -110x + -110x + 4x2

Combine like terms: -110x + -110x = -220x
2x2 = 2704 + -220x + 4x2

Solving
2x2 = 2704 + -220x + 4x2

Solving for variable 'x'.

Reorder the terms:
-2704 + 220x + 2x2 + -4x2 = 2704 + -220x + 4x2 + -2704 + 220x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
-2704 + 220x + -2x2 = 2704 + -220x + 4x2 + -2704 + 220x + -4x2

Reorder the terms:
-2704 + 220x + -2x2 = 2704 + -2704 + -220x + 220x + 4x2 + -4x2

Combine like terms: 2704 + -2704 = 0
-2704 + 220x + -2x2 = 0 + -220x + 220x + 4x2 + -4x2
-2704 + 220x + -2x2 = -220x + 220x + 4x2 + -4x2

Combine like terms: -220x + 220x = 0
-2704 + 220x + -2x2 = 0 + 4x2 + -4x2
-2704 + 220x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-2704 + 220x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1352 + 110x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1352 + 110x + -1x2)' equal to zero and attempt to solve:

Simplifying
-1352 + 110x + -1x2 = 0

Solving
-1352 + 110x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1352 + -110x + x2 = 0

Move the constant term to the right:

Add '-1352' to each side of the equation.
1352 + -110x + -1352 + x2 = 0 + -1352

Reorder the terms:
1352 + -1352 + -110x + x2 = 0 + -1352

Combine like terms: 1352 + -1352 = 0
0 + -110x + x2 = 0 + -1352
-110x + x2 = 0 + -1352

Combine like terms: 0 + -1352 = -1352
-110x + x2 = -1352

The x term is -110x.  Take half its coefficient (-55).
Square it (3025) and add it to both sides.

Add '3025' to each side of the equation.
-110x + 3025 + x2 = -1352 + 3025

Reorder the terms:
3025 + -110x + x2 = -1352 + 3025

Combine like terms: -1352 + 3025 = 1673
3025 + -110x + x2 = 1673

Factor a perfect square on the left side:
(x + -55)(x + -55) = 1673

Calculate the square root of the right side: 40.902322672

Break this problem into two subproblems by setting 
(x + -55) equal to 40.902322672 and -40.902322672.

Subproblem 1
x + -55 = 40.902322672

Simplifying
x + -55 = 40.902322672

Reorder the terms:
-55 + x = 40.902322672

Solving
-55 + x = 40.902322672

Solving for variable 'x'.

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

Add '55' to each side of the equation.
-55 + 55 + x = 40.902322672 + 55

Combine like terms: -55 + 55 = 0
0 + x = 40.902322672 + 55
x = 40.902322672 + 55

Combine like terms: 40.902322672 + 55 = 95.902322672
x = 95.902322672

Simplifying
x = 95.902322672

Subproblem 2
x + -55 = -40.902322672

Simplifying
x + -55 = -40.902322672

Reorder the terms:
-55 + x = -40.902322672

Solving
-55 + x = -40.902322672

Solving for variable 'x'.

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

Add '55' to each side of the equation.
-55 + 55 + x = -40.902322672 + 55

Combine like terms: -55 + 55 = 0
0 + x = -40.902322672 + 55
x = -40.902322672 + 55

Combine like terms: -40.902322672 + 55 = 14.097677328
x = 14.097677328

Simplifying
x = 14.097677328

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {95.902322672, 14.097677328}
Solution
x = {95.902322672, 14.097677328}