u^2-20u-8=0

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Solution for u^2-20u-8=0 equation: 


Simplifying
u2 + -20u + -8 = 0

Reorder the terms:
-8 + -20u + u2 = 0

Solving
-8 + -20u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -20u + 8 + u2 = 0 + 8

Reorder the terms:
-8 + 8 + -20u + u2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -20u + u2 = 0 + 8
-20u + u2 = 0 + 8

Combine like terms: 0 + 8 = 8
-20u + u2 = 8

The u term is -20u.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20u + 100 + u2 = 8 + 100

Reorder the terms:
100 + -20u + u2 = 8 + 100

Combine like terms: 8 + 100 = 108
100 + -20u + u2 = 108

Factor a perfect square on the left side:
(u + -10)(u + -10) = 108

Calculate the square root of the right side: 10.392304845

Break this problem into two subproblems by setting 
(u + -10) equal to 10.392304845 and -10.392304845.


Subproblem 1
u + -10 = 10.392304845

Simplifying
u + -10 = 10.392304845

Reorder the terms:
-10 + u = 10.392304845

Solving
-10 + u = 10.392304845

Solving for variable 'u'.

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

Add '10' to each side of the equation.
-10 + 10 + u = 10.392304845 + 10

Combine like terms: -10 + 10 = 0
0 + u = 10.392304845 + 10
u = 10.392304845 + 10

Combine like terms: 10.392304845 + 10 = 20.392304845
u = 20.392304845

Simplifying
u = 20.392304845


Subproblem 2
u + -10 = -10.392304845

Simplifying
u + -10 = -10.392304845

Reorder the terms:
-10 + u = -10.392304845

Solving
-10 + u = -10.392304845

Solving for variable 'u'.

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

Add '10' to each side of the equation.
-10 + 10 + u = -10.392304845 + 10

Combine like terms: -10 + 10 = 0
0 + u = -10.392304845 + 10
u = -10.392304845 + 10

Combine like terms: -10.392304845 + 10 = -0.392304845
u = -0.392304845

Simplifying
u = -0.392304845


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {20.392304845, -0.392304845}

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