u^2-4u-23=0

Solution for u^2-4u-23=0 equation:

Simplifying
u2 + -4u + -23 = 0

Reorder the terms:
-23 + -4u + u2 = 0

Solving
-23 + -4u + 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 + -4u + 23 + u2 = 0 + 23

Reorder the terms:
-23 + 23 + -4u + u2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -4u + u2 = 0 + 23
-4u + u2 = 0 + 23

Combine like terms: 0 + 23 = 23
-4u + u2 = 23

The u term is -4u.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4u + 4 + u2 = 23 + 4

Reorder the terms:
4 + -4u + u2 = 23 + 4

Combine like terms: 23 + 4 = 27
4 + -4u + u2 = 27

Factor a perfect square on the left side:
(u + -2)(u + -2) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(u + -2) equal to 5.196152423 and -5.196152423.

Subproblem 1
u + -2 = 5.196152423

Simplifying
u + -2 = 5.196152423

Reorder the terms:
-2 + u = 5.196152423

Solving
-2 + u = 5.196152423

Solving for variable 'u'.

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

Add '2' to each side of the equation.
-2 + 2 + u = 5.196152423 + 2

Combine like terms: -2 + 2 = 0
0 + u = 5.196152423 + 2
u = 5.196152423 + 2

Combine like terms: 5.196152423 + 2 = 7.196152423
u = 7.196152423

Simplifying
u = 7.196152423

Subproblem 2
u + -2 = -5.196152423

Simplifying
u + -2 = -5.196152423

Reorder the terms:
-2 + u = -5.196152423

Solving
-2 + u = -5.196152423

Solving for variable 'u'.

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

Add '2' to each side of the equation.
-2 + 2 + u = -5.196152423 + 2

Combine like terms: -2 + 2 = 0
0 + u = -5.196152423 + 2
u = -5.196152423 + 2

Combine like terms: -5.196152423 + 2 = -3.196152423
u = -3.196152423

Simplifying
u = -3.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {7.196152423, -3.196152423}