u^2+20u+11=0

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Solution for u^2+20u+11=0 equation: 


Simplifying
u2 + 20u + 11 = 0

Reorder the terms:
11 + 20u + u2 = 0

Solving
11 + 20u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 20u + -11 + u2 = 0 + -11

Reorder the terms:
11 + -11 + 20u + u2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 20u + u2 = 0 + -11
20u + u2 = 0 + -11

Combine like terms: 0 + -11 = -11
20u + u2 = -11

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 = -11 + 100

Reorder the terms:
100 + 20u + u2 = -11 + 100

Combine like terms: -11 + 100 = 89
100 + 20u + u2 = 89

Factor a perfect square on the left side:
(u + 10)(u + 10) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(u + 10) equal to 9.433981132 and -9.433981132.


Subproblem 1
u + 10 = 9.433981132

Simplifying
u + 10 = 9.433981132

Reorder the terms:
10 + u = 9.433981132

Solving
10 + u = 9.433981132

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 = 9.433981132 + -10

Combine like terms: 10 + -10 = 0
0 + u = 9.433981132 + -10
u = 9.433981132 + -10

Combine like terms: 9.433981132 + -10 = -0.566018868
u = -0.566018868

Simplifying
u = -0.566018868


Subproblem 2
u + 10 = -9.433981132

Simplifying
u + 10 = -9.433981132

Reorder the terms:
10 + u = -9.433981132

Solving
10 + u = -9.433981132

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 = -9.433981132 + -10

Combine like terms: 10 + -10 = 0
0 + u = -9.433981132 + -10
u = -9.433981132 + -10

Combine like terms: -9.433981132 + -10 = -19.433981132
u = -19.433981132

Simplifying
u = -19.433981132


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-0.566018868, -19.433981132}

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