u^2-13u-23=0

Solution for u^2-13u-23=0 equation:

Simplifying
u2 + -13u + -23 = 0

Reorder the terms:
-23 + -13u + u2 = 0

Solving
-23 + -13u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + -13u + 23 + u2 = 0 + 23

Reorder the terms:
-23 + 23 + -13u + u2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -13u + u2 = 0 + 23
-13u + u2 = 0 + 23

Combine like terms: 0 + 23 = 23
-13u + u2 = 23

The u term is -13u.  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.
-13u + 42.25 + u2 = 23 + 42.25

Reorder the terms:
42.25 + -13u + u2 = 23 + 42.25

Combine like terms: 23 + 42.25 = 65.25
42.25 + -13u + u2 = 65.25

Factor a perfect square on the left side:
(u + -6.5)(u + -6.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(u + -6.5) equal to 8.077747211 and -8.077747211.

Subproblem 1
u + -6.5 = 8.077747211

Simplifying
u + -6.5 = 8.077747211

Reorder the terms:
-6.5 + u = 8.077747211

Solving
-6.5 + u = 8.077747211

Solving for variable 'u'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + u = 8.077747211 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + u = 8.077747211 + 6.5
u = 8.077747211 + 6.5

Combine like terms: 8.077747211 + 6.5 = 14.577747211
u = 14.577747211

Simplifying
u = 14.577747211

Subproblem 2
u + -6.5 = -8.077747211

Simplifying
u + -6.5 = -8.077747211

Reorder the terms:
-6.5 + u = -8.077747211

Solving
-6.5 + u = -8.077747211

Solving for variable 'u'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + u = -8.077747211 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + u = -8.077747211 + 6.5
u = -8.077747211 + 6.5

Combine like terms: -8.077747211 + 6.5 = -1.577747211
u = -1.577747211

Simplifying
u = -1.577747211

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {14.577747211, -1.577747211}