u^2-5u-4=0

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Solution for u^2-5u-4=0 equation: 


Simplifying
u2 + -5u + -4 = 0

Reorder the terms:
-4 + -5u + u2 = 0

Solving
-4 + -5u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -5u + 4 + u2 = 0 + 4

Reorder the terms:
-4 + 4 + -5u + u2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5u + u2 = 0 + 4
-5u + u2 = 0 + 4

Combine like terms: 0 + 4 = 4
-5u + u2 = 4

The u term is -5u.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5u + 6.25 + u2 = 4 + 6.25

Reorder the terms:
6.25 + -5u + u2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + -5u + u2 = 10.25

Factor a perfect square on the left side:
(u + -2.5)(u + -2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(u + -2.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
u + -2.5 = 3.201562119

Simplifying
u + -2.5 = 3.201562119

Reorder the terms:
-2.5 + u = 3.201562119

Solving
-2.5 + u = 3.201562119

Solving for variable 'u'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + u = 3.201562119 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + u = 3.201562119 + 2.5
u = 3.201562119 + 2.5

Combine like terms: 3.201562119 + 2.5 = 5.701562119
u = 5.701562119

Simplifying
u = 5.701562119


Subproblem 2
u + -2.5 = -3.201562119

Simplifying
u + -2.5 = -3.201562119

Reorder the terms:
-2.5 + u = -3.201562119

Solving
-2.5 + u = -3.201562119

Solving for variable 'u'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + u = -3.201562119 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + u = -3.201562119 + 2.5
u = -3.201562119 + 2.5

Combine like terms: -3.201562119 + 2.5 = -0.701562119
u = -0.701562119

Simplifying
u = -0.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {5.701562119, -0.701562119}

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