u^2-8u+5=0

Solution for u^2-8u+5=0 equation:

Simplifying
u2 + -8u + 5 = 0

Reorder the terms:
5 + -8u + u2 = 0

Solving
5 + -8u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -8u + -5 + u2 = 0 + -5

Reorder the terms:
5 + -5 + -8u + u2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8u + u2 = 0 + -5
-8u + u2 = 0 + -5

Combine like terms: 0 + -5 = -5
-8u + u2 = -5

The u term is -8u.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8u + 16 + u2 = -5 + 16

Reorder the terms:
16 + -8u + u2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + -8u + u2 = 11

Factor a perfect square on the left side:
(u + -4)(u + -4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(u + -4) equal to 3.31662479 and -3.31662479.

Subproblem 1
u + -4 = 3.31662479

Simplifying
u + -4 = 3.31662479

Reorder the terms:
-4 + u = 3.31662479

Solving
-4 + u = 3.31662479

Solving for variable 'u'.

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

Add '4' to each side of the equation.
-4 + 4 + u = 3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + u = 3.31662479 + 4
u = 3.31662479 + 4

Combine like terms: 3.31662479 + 4 = 7.31662479
u = 7.31662479

Simplifying
u = 7.31662479

Subproblem 2
u + -4 = -3.31662479

Simplifying
u + -4 = -3.31662479

Reorder the terms:
-4 + u = -3.31662479

Solving
-4 + u = -3.31662479

Solving for variable 'u'.

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

Add '4' to each side of the equation.
-4 + 4 + u = -3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + u = -3.31662479 + 4
u = -3.31662479 + 4

Combine like terms: -3.31662479 + 4 = 0.68337521
u = 0.68337521

Simplifying
u = 0.68337521

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {7.31662479, 0.68337521}