2601=441+2x+2x^2

Solution for 2601=441+2x+2x^2 equation:

Simplifying
2601 = 441 + 2x + 2x2

Solving
2601 = 441 + 2x + 2x2

Solving for variable 'x'.

Combine like terms: 2601 + -441 = 2160
2160 + -2x + -2x2 = 441 + 2x + 2x2 + -441 + -2x + -2x2

Reorder the terms:
2160 + -2x + -2x2 = 441 + -441 + 2x + -2x + 2x2 + -2x2

Combine like terms: 441 + -441 = 0
2160 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2
2160 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
2160 + -2x + -2x2 = 0 + 2x2 + -2x2
2160 + -2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
2160 + -2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1080 + -1x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1080 + -1x + -1x2)' equal to zero and attempt to solve:

Simplifying
1080 + -1x + -1x2 = 0

Solving
1080 + -1x + -1x2 = 0

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

Divide each side by '-1'.
-1080 + x + x2 = 0

Move the constant term to the right:

Add '1080' to each side of the equation.
-1080 + x + 1080 + x2 = 0 + 1080

Reorder the terms:
-1080 + 1080 + x + x2 = 0 + 1080

Combine like terms: -1080 + 1080 = 0
0 + x + x2 = 0 + 1080
x + x2 = 0 + 1080

Combine like terms: 0 + 1080 = 1080
x + x2 = 1080

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.
 + 0.25 + x2 = 1080 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1080 + 0.25

Combine like terms: 1080 + 0.25 = 1080.25
1.25 + x2 = 1080.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1080.25

Calculate the square root of the right side: 32.867156859

Break this problem into two subproblems by setting 
(x + 0.5) equal to 32.867156859 and -32.867156859.

Subproblem 1
x + 0.5 = 32.867156859

Simplifying
x + 0.5 = 32.867156859

Reorder the terms:
0.5 + x = 32.867156859

Solving
0.5 + x = 32.867156859

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 = 32.867156859 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 32.867156859 + -0.5
x = 32.867156859 + -0.5

Combine like terms: 32.867156859 + -0.5 = 32.367156859
x = 32.367156859

Simplifying
x = 32.367156859

Subproblem 2
x + 0.5 = -32.867156859

Simplifying
x + 0.5 = -32.867156859

Reorder the terms:
0.5 + x = -32.867156859

Solving
0.5 + x = -32.867156859

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 = -32.867156859 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -32.867156859 + -0.5
x = -32.867156859 + -0.5

Combine like terms: -32.867156859 + -0.5 = -33.367156859
x = -33.367156859

Simplifying
x = -33.367156859

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {32.367156859, -33.367156859}
Solution
x = {32.367156859, -33.367156859}