x^2-2x+3x-26=105

Solution for x^2-2x+3x-26=105 equation:

Simplifying
x2 + -2x + 3x + -26 = 105

Reorder the terms:
-26 + -2x + 3x + x2 = 105

Combine like terms: -2x + 3x = 1x
-26 + 1x + x2 = 105

Solving
-26 + 1x + x2 = 105

Solving for variable 'x'.

Reorder the terms:
-26 + -105 + 1x + x2 = 105 + -105

Combine like terms: -26 + -105 = -131
-131 + 1x + x2 = 105 + -105

Combine like terms: 105 + -105 = 0
-131 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '131' to each side of the equation.
-131 + 1x + 131 + x2 = 0 + 131

Reorder the terms:
-131 + 131 + 1x + x2 = 0 + 131

Combine like terms: -131 + 131 = 0
0 + 1x + x2 = 0 + 131
1x + x2 = 0 + 131

Combine like terms: 0 + 131 = 131
1x + x2 = 131

The x term is 1x.  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.
x + 0.25 + x2 = 131 + 0.25

Reorder the terms:
0.25 + x + x2 = 131 + 0.25

Combine like terms: 131 + 0.25 = 131.25
0.25 + x + x2 = 131.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 131.25

Calculate the square root of the right side: 11.456439237

Break this problem into two subproblems by setting 
(x + 0.5) equal to 11.456439237 and -11.456439237.

Subproblem 1
x + 0.5 = 11.456439237

Simplifying
x + 0.5 = 11.456439237

Reorder the terms:
0.5 + x = 11.456439237

Solving
0.5 + x = 11.456439237

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 = 11.456439237 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 11.456439237 + -0.5
x = 11.456439237 + -0.5

Combine like terms: 11.456439237 + -0.5 = 10.956439237
x = 10.956439237

Simplifying
x = 10.956439237

Subproblem 2
x + 0.5 = -11.456439237

Simplifying
x + 0.5 = -11.456439237

Reorder the terms:
0.5 + x = -11.456439237

Solving
0.5 + x = -11.456439237

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 = -11.456439237 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -11.456439237 + -0.5
x = -11.456439237 + -0.5

Combine like terms: -11.456439237 + -0.5 = -11.956439237
x = -11.956439237

Simplifying
x = -11.956439237

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.956439237, -11.956439237}