4u^2+44u=148

Solution for 4u^2+44u=148 equation:

Simplifying
4u2 + 44u = 148

Reorder the terms:
44u + 4u2 = 148

Solving
44u + 4u2 = 148

Solving for variable 'u'.

Reorder the terms:
-148 + 44u + 4u2 = 148 + -148

Combine like terms: 148 + -148 = 0
-148 + 44u + 4u2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-37 + 11u + u2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-37 + 11u + u2)' equal to zero and attempt to solve:

Simplifying
-37 + 11u + u2 = 0

Solving
-37 + 11u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 11u + 37 + u2 = 0 + 37

Reorder the terms:
-37 + 37 + 11u + u2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 11u + u2 = 0 + 37
11u + u2 = 0 + 37

Combine like terms: 0 + 37 = 37
11u + u2 = 37

The u term is 11u.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11u + 30.25 + u2 = 37 + 30.25

Reorder the terms:
30.25 + 11u + u2 = 37 + 30.25

Combine like terms: 37 + 30.25 = 67.25
30.25 + 11u + u2 = 67.25

Factor a perfect square on the left side:
(u + 5.5)(u + 5.5) = 67.25

Calculate the square root of the right side: 8.200609733

Break this problem into two subproblems by setting 
(u + 5.5) equal to 8.200609733 and -8.200609733.

Subproblem 1
u + 5.5 = 8.200609733

Simplifying
u + 5.5 = 8.200609733

Reorder the terms:
5.5 + u = 8.200609733

Solving
5.5 + u = 8.200609733

Solving for variable 'u'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + u = 8.200609733 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + u = 8.200609733 + -5.5
u = 8.200609733 + -5.5

Combine like terms: 8.200609733 + -5.5 = 2.700609733
u = 2.700609733

Simplifying
u = 2.700609733

Subproblem 2
u + 5.5 = -8.200609733

Simplifying
u + 5.5 = -8.200609733

Reorder the terms:
5.5 + u = -8.200609733

Solving
5.5 + u = -8.200609733

Solving for variable 'u'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + u = -8.200609733 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + u = -8.200609733 + -5.5
u = -8.200609733 + -5.5

Combine like terms: -8.200609733 + -5.5 = -13.700609733
u = -13.700609733

Simplifying
u = -13.700609733

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {2.700609733, -13.700609733}
Solution
u = {2.700609733, -13.700609733}