5u^2-55u-8=0

Solution for 5u^2-55u-8=0 equation:

Simplifying
5u2 + -55u + -8 = 0

Reorder the terms:
-8 + -55u + 5u2 = 0

Solving
-8 + -55u + 5u2 = 0

Solving for variable 'u'.

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

Divide each side by '5'.
-1.6 + -11u + u2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -11u + 1.6 + u2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -11u + u2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -11u + u2 = 0 + 1.6
-11u + u2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-11u + u2 = 1.6

The u term is -11u.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11u + 30.25 + u2 = 1.6 + 30.25

Reorder the terms:
30.25 + -11u + u2 = 1.6 + 30.25

Combine like terms: 1.6 + 30.25 = 31.85
30.25 + -11u + u2 = 31.85

Factor a perfect square on the left side:
(u + -5.5)(u + -5.5) = 31.85

Calculate the square root of the right side: 5.643580424

Break this problem into two subproblems by setting 
(u + -5.5) equal to 5.643580424 and -5.643580424.

Subproblem 1
u + -5.5 = 5.643580424

Simplifying
u + -5.5 = 5.643580424

Reorder the terms:
-5.5 + u = 5.643580424

Solving
-5.5 + u = 5.643580424

Solving for variable 'u'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + u = 5.643580424 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + u = 5.643580424 + 5.5
u = 5.643580424 + 5.5

Combine like terms: 5.643580424 + 5.5 = 11.143580424
u = 11.143580424

Simplifying
u = 11.143580424

Subproblem 2
u + -5.5 = -5.643580424

Simplifying
u + -5.5 = -5.643580424

Reorder the terms:
-5.5 + u = -5.643580424

Solving
-5.5 + u = -5.643580424

Solving for variable 'u'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + u = -5.643580424 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + u = -5.643580424 + 5.5
u = -5.643580424 + 5.5

Combine like terms: -5.643580424 + 5.5 = -0.143580424
u = -0.143580424

Simplifying
u = -0.143580424

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {11.143580424, -0.143580424}