0=u^2-5u-2

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


Simplifying
0 = u2 + -5u + -2

Reorder the terms:
0 = -2 + -5u + u2

Solving
0 = -2 + -5u + u2

Solving for variable 'u'.

Combine like terms: 0 + 2 = 2
2 + 5u + -1u2 = -2 + -5u + u2 + 2 + 5u + -1u2

Reorder the terms:
2 + 5u + -1u2 = -2 + 2 + -5u + 5u + u2 + -1u2

Combine like terms: -2 + 2 = 0
2 + 5u + -1u2 = 0 + -5u + 5u + u2 + -1u2
2 + 5u + -1u2 = -5u + 5u + u2 + -1u2

Combine like terms: -5u + 5u = 0
2 + 5u + -1u2 = 0 + u2 + -1u2
2 + 5u + -1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
2 + 5u + -1u2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -5u + u2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -5u + 2 + u2 = 0 + 2

Reorder the terms:
-2 + 2 + -5u + u2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5u + u2 = 0 + 2
-5u + u2 = 0 + 2

Combine like terms: 0 + 2 = 2
-5u + u2 = 2

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 = 2 + 6.25

Reorder the terms:
6.25 + -5u + u2 = 2 + 6.25

Combine like terms: 2 + 6.25 = 8.25
6.25 + -5u + u2 = 8.25

Factor a perfect square on the left side:
(u + -2.5)(u + -2.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(u + -2.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
u + -2.5 = 2.872281323

Simplifying
u + -2.5 = 2.872281323

Reorder the terms:
-2.5 + u = 2.872281323

Solving
-2.5 + u = 2.872281323

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 = 2.872281323 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + u = 2.872281323 + 2.5
u = 2.872281323 + 2.5

Combine like terms: 2.872281323 + 2.5 = 5.372281323
u = 5.372281323

Simplifying
u = 5.372281323


Subproblem 2
u + -2.5 = -2.872281323

Simplifying
u + -2.5 = -2.872281323

Reorder the terms:
-2.5 + u = -2.872281323

Solving
-2.5 + u = -2.872281323

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 = -2.872281323 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + u = -2.872281323 + 2.5
u = -2.872281323 + 2.5

Combine like terms: -2.872281323 + 2.5 = -0.372281323
u = -0.372281323

Simplifying
u = -0.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {5.372281323, -0.372281323}

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