2(w+11)(w)=320

Solution for 2(w+11)(w)=320 equation:

Simplifying
2(w + 11)(w) = 320

Reorder the terms:
2(11 + w)(w) = 320

Reorder the terms for easier multiplication:
2w(11 + w) = 320
(11 * 2w + w * 2w) = 320
(22w + 2w2) = 320

Solving
22w + 2w2 = 320

Solving for variable 'w'.

Reorder the terms:
-320 + 22w + 2w2 = 320 + -320

Combine like terms: 320 + -320 = 0
-320 + 22w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-160 + 11w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-160 + 11w + w2)' equal to zero and attempt to solve:

Simplifying
-160 + 11w + w2 = 0

Solving
-160 + 11w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + 11w + 160 + w2 = 0 + 160

Reorder the terms:
-160 + 160 + 11w + w2 = 0 + 160

Combine like terms: -160 + 160 = 0
0 + 11w + w2 = 0 + 160
11w + w2 = 0 + 160

Combine like terms: 0 + 160 = 160
11w + w2 = 160

The w term is 11w.  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.
11w + 30.25 + w2 = 160 + 30.25

Reorder the terms:
30.25 + 11w + w2 = 160 + 30.25

Combine like terms: 160 + 30.25 = 190.25
30.25 + 11w + w2 = 190.25

Factor a perfect square on the left side:
(w + 5.5)(w + 5.5) = 190.25

Calculate the square root of the right side: 13.793114224

Break this problem into two subproblems by setting 
(w + 5.5) equal to 13.793114224 and -13.793114224.

Subproblem 1
w + 5.5 = 13.793114224

Simplifying
w + 5.5 = 13.793114224

Reorder the terms:
5.5 + w = 13.793114224

Solving
5.5 + w = 13.793114224

Solving for variable 'w'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + w = 13.793114224 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + w = 13.793114224 + -5.5
w = 13.793114224 + -5.5

Combine like terms: 13.793114224 + -5.5 = 8.293114224
w = 8.293114224

Simplifying
w = 8.293114224

Subproblem 2
w + 5.5 = -13.793114224

Simplifying
w + 5.5 = -13.793114224

Reorder the terms:
5.5 + w = -13.793114224

Solving
5.5 + w = -13.793114224

Solving for variable 'w'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + w = -13.793114224 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + w = -13.793114224 + -5.5
w = -13.793114224 + -5.5

Combine like terms: -13.793114224 + -5.5 = -19.293114224
w = -19.293114224

Simplifying
w = -19.293114224

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.293114224, -19.293114224}
Solution
w = {8.293114224, -19.293114224}