2x^2-26x=-23

Solution for 2x^2-26x=-23 equation:

Simplifying
2x2 + -26x = -23

Reorder the terms:
-26x + 2x2 = -23

Solving
-26x + 2x2 = -23

Solving for variable 'x'.

Reorder the terms:
23 + -26x + 2x2 = -23 + 23

Combine like terms: -23 + 23 = 0
23 + -26x + 2x2 = 0

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

Divide each side by '2'.
11.5 + -13x + x2 = 0

Move the constant term to the right:

Add '-11.5' to each side of the equation.
11.5 + -13x + -11.5 + x2 = 0 + -11.5

Reorder the terms:
11.5 + -11.5 + -13x + x2 = 0 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + -13x + x2 = 0 + -11.5
-13x + x2 = 0 + -11.5

Combine like terms: 0 + -11.5 = -11.5
-13x + x2 = -11.5

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -11.5 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -11.5 + 42.25

Combine like terms: -11.5 + 42.25 = 30.75
42.25 + -13x + x2 = 30.75

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 30.75

Calculate the square root of the right side: 5.545268253

Break this problem into two subproblems by setting 
(x + -6.5) equal to 5.545268253 and -5.545268253.

Subproblem 1
x + -6.5 = 5.545268253

Simplifying
x + -6.5 = 5.545268253

Reorder the terms:
-6.5 + x = 5.545268253

Solving
-6.5 + x = 5.545268253

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 5.545268253 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 5.545268253 + 6.5
x = 5.545268253 + 6.5

Combine like terms: 5.545268253 + 6.5 = 12.045268253
x = 12.045268253

Simplifying
x = 12.045268253

Subproblem 2
x + -6.5 = -5.545268253

Simplifying
x + -6.5 = -5.545268253

Reorder the terms:
-6.5 + x = -5.545268253

Solving
-6.5 + x = -5.545268253

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -5.545268253 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -5.545268253 + 6.5
x = -5.545268253 + 6.5

Combine like terms: -5.545268253 + 6.5 = 0.954731747
x = 0.954731747

Simplifying
x = 0.954731747

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.045268253, 0.954731747}