x^2-44x+105=0

Solution for x^2-44x+105=0 equation:

Simplifying
x2 + -44x + 105 = 0

Reorder the terms:
105 + -44x + x2 = 0

Solving
105 + -44x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-105' to each side of the equation.
105 + -44x + -105 + x2 = 0 + -105

Reorder the terms:
105 + -105 + -44x + x2 = 0 + -105

Combine like terms: 105 + -105 = 0
0 + -44x + x2 = 0 + -105
-44x + x2 = 0 + -105

Combine like terms: 0 + -105 = -105
-44x + x2 = -105

The x term is -44x.  Take half its coefficient (-22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
-44x + 484 + x2 = -105 + 484

Reorder the terms:
484 + -44x + x2 = -105 + 484

Combine like terms: -105 + 484 = 379
484 + -44x + x2 = 379

Factor a perfect square on the left side:
(x + -22)(x + -22) = 379

Calculate the square root of the right side: 19.467922334

Break this problem into two subproblems by setting 
(x + -22) equal to 19.467922334 and -19.467922334.

Subproblem 1
x + -22 = 19.467922334

Simplifying
x + -22 = 19.467922334

Reorder the terms:
-22 + x = 19.467922334

Solving
-22 + x = 19.467922334

Solving for variable 'x'.

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

Add '22' to each side of the equation.
-22 + 22 + x = 19.467922334 + 22

Combine like terms: -22 + 22 = 0
0 + x = 19.467922334 + 22
x = 19.467922334 + 22

Combine like terms: 19.467922334 + 22 = 41.467922334
x = 41.467922334

Simplifying
x = 41.467922334

Subproblem 2
x + -22 = -19.467922334

Simplifying
x + -22 = -19.467922334

Reorder the terms:
-22 + x = -19.467922334

Solving
-22 + x = -19.467922334

Solving for variable 'x'.

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

Add '22' to each side of the equation.
-22 + 22 + x = -19.467922334 + 22

Combine like terms: -22 + 22 = 0
0 + x = -19.467922334 + 22
x = -19.467922334 + 22

Combine like terms: -19.467922334 + 22 = 2.532077666
x = 2.532077666

Simplifying
x = 2.532077666

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {41.467922334, 2.532077666}