u^2-3u-1=0

Solution for u^2-3u-1=0 equation:

Simplifying
u2 + -3u + -1 = 0

Reorder the terms:
-1 + -3u + u2 = 0

Solving
-1 + -3u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3u + 1 + u2 = 0 + 1

Reorder the terms:
-1 + 1 + -3u + u2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3u + u2 = 0 + 1
-3u + u2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3u + u2 = 1

The u term is -3u.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3u + 2.25 + u2 = 1 + 2.25

Reorder the terms:
2.25 + -3u + u2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + -3u + u2 = 3.25

Factor a perfect square on the left side:
(u + -1.5)(u + -1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(u + -1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
u + -1.5 = 1.802775638

Simplifying
u + -1.5 = 1.802775638

Reorder the terms:
-1.5 + u = 1.802775638

Solving
-1.5 + u = 1.802775638

Solving for variable 'u'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + u = 1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = 1.802775638 + 1.5
u = 1.802775638 + 1.5

Combine like terms: 1.802775638 + 1.5 = 3.302775638
u = 3.302775638

Simplifying
u = 3.302775638

Subproblem 2
u + -1.5 = -1.802775638

Simplifying
u + -1.5 = -1.802775638

Reorder the terms:
-1.5 + u = -1.802775638

Solving
-1.5 + u = -1.802775638

Solving for variable 'u'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + u = -1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = -1.802775638 + 1.5
u = -1.802775638 + 1.5

Combine like terms: -1.802775638 + 1.5 = -0.302775638
u = -0.302775638

Simplifying
u = -0.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {3.302775638, -0.302775638}