u^2+22u+11=0

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Solution for u^2+22u+11=0 equation: 


Simplifying
u2 + 22u + 11 = 0

Reorder the terms:
11 + 22u + u2 = 0

Solving
11 + 22u + 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 + 22u + -11 + u2 = 0 + -11

Reorder the terms:
11 + -11 + 22u + u2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 22u + u2 = 0 + -11
22u + u2 = 0 + -11

Combine like terms: 0 + -11 = -11
22u + u2 = -11

The u term is 22u.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22u + 121 + u2 = -11 + 121

Reorder the terms:
121 + 22u + u2 = -11 + 121

Combine like terms: -11 + 121 = 110
121 + 22u + u2 = 110

Factor a perfect square on the left side:
(u + 11)(u + 11) = 110

Calculate the square root of the right side: 10.488088482

Break this problem into two subproblems by setting 
(u + 11) equal to 10.488088482 and -10.488088482.


Subproblem 1
u + 11 = 10.488088482

Simplifying
u + 11 = 10.488088482

Reorder the terms:
11 + u = 10.488088482

Solving
11 + u = 10.488088482

Solving for variable 'u'.

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

Add '-11' to each side of the equation.
11 + -11 + u = 10.488088482 + -11

Combine like terms: 11 + -11 = 0
0 + u = 10.488088482 + -11
u = 10.488088482 + -11

Combine like terms: 10.488088482 + -11 = -0.511911518
u = -0.511911518

Simplifying
u = -0.511911518


Subproblem 2
u + 11 = -10.488088482

Simplifying
u + 11 = -10.488088482

Reorder the terms:
11 + u = -10.488088482

Solving
11 + u = -10.488088482

Solving for variable 'u'.

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

Add '-11' to each side of the equation.
11 + -11 + u = -10.488088482 + -11

Combine like terms: 11 + -11 = 0
0 + u = -10.488088482 + -11
u = -10.488088482 + -11

Combine like terms: -10.488088482 + -11 = -21.488088482
u = -21.488088482

Simplifying
u = -21.488088482


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-0.511911518, -21.488088482}

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