4u^2+32u+22=0

Solution for 4u^2+32u+22=0 equation:

Simplifying
4u2 + 32u + 22 = 0

Reorder the terms:
22 + 32u + 4u2 = 0

Solving
22 + 32u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + 16u + 2u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + 16u + 2u2)' equal to zero and attempt to solve:

Simplifying
11 + 16u + 2u2 = 0

Solving
11 + 16u + 2u2 = 0

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

Divide each side by '2'.
5.5 + 8u + u2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + 8u + -5.5 + u2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + 8u + u2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + 8u + u2 = 0 + -5.5
8u + u2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
8u + u2 = -5.5

The u term is 8u.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8u + 16 + u2 = -5.5 + 16

Reorder the terms:
16 + 8u + u2 = -5.5 + 16

Combine like terms: -5.5 + 16 = 10.5
16 + 8u + u2 = 10.5

Factor a perfect square on the left side:
(u + 4)(u + 4) = 10.5

Calculate the square root of the right side: 3.240370349

Break this problem into two subproblems by setting 
(u + 4) equal to 3.240370349 and -3.240370349.

Subproblem 1
u + 4 = 3.240370349

Simplifying
u + 4 = 3.240370349

Reorder the terms:
4 + u = 3.240370349

Solving
4 + u = 3.240370349

Solving for variable 'u'.

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

Add '-4' to each side of the equation.
4 + -4 + u = 3.240370349 + -4

Combine like terms: 4 + -4 = 0
0 + u = 3.240370349 + -4
u = 3.240370349 + -4

Combine like terms: 3.240370349 + -4 = -0.759629651
u = -0.759629651

Simplifying
u = -0.759629651

Subproblem 2
u + 4 = -3.240370349

Simplifying
u + 4 = -3.240370349

Reorder the terms:
4 + u = -3.240370349

Solving
4 + u = -3.240370349

Solving for variable 'u'.

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

Add '-4' to each side of the equation.
4 + -4 + u = -3.240370349 + -4

Combine like terms: 4 + -4 = 0
0 + u = -3.240370349 + -4
u = -3.240370349 + -4

Combine like terms: -3.240370349 + -4 = -7.240370349
u = -7.240370349

Simplifying
u = -7.240370349

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-0.759629651, -7.240370349}
Solution
u = {-0.759629651, -7.240370349}