244=2w(4w+4)

Solution for 244=2w(4w+4) equation:

Simplifying
244 = 2w(4w + 4)

Reorder the terms:
244 = 2w(4 + 4w)
244 = (4 * 2w + 4w * 2w)
244 = (8w + 8w2)

Solving
244 = 8w + 8w2

Solving for variable 'w'.

Reorder the terms:
244 + -8w + -8w2 = 8w + -8w + 8w2 + -8w2

Combine like terms: 8w + -8w = 0
244 + -8w + -8w2 = 0 + 8w2 + -8w2
244 + -8w + -8w2 = 8w2 + -8w2

Combine like terms: 8w2 + -8w2 = 0
244 + -8w + -8w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(61 + -2w + -2w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(61 + -2w + -2w2)' equal to zero and attempt to solve:

Simplifying
61 + -2w + -2w2 = 0

Solving
61 + -2w + -2w2 = 0

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

Divide each side by '-2'.
-30.5 + w + w2 = 0

Move the constant term to the right:

Add '30.5' to each side of the equation.
-30.5 + w + 30.5 + w2 = 0 + 30.5

Reorder the terms:
-30.5 + 30.5 + w + w2 = 0 + 30.5

Combine like terms: -30.5 + 30.5 = 0.0
0.0 + w + w2 = 0 + 30.5
w + w2 = 0 + 30.5

Combine like terms: 0 + 30.5 = 30.5
w + w2 = 30.5

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + w2 = 30.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + w2 = 30.5 + 0.25

Combine like terms: 30.5 + 0.25 = 30.75
1.25 + w2 = 30.75

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 30.75

Calculate the square root of the right side: 5.545268253

Break this problem into two subproblems by setting 
(w + 0.5) equal to 5.545268253 and -5.545268253.

Subproblem 1
w + 0.5 = 5.545268253

Simplifying
w + 0.5 = 5.545268253

Reorder the terms:
0.5 + w = 5.545268253

Solving
0.5 + w = 5.545268253

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 5.545268253 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 5.545268253 + -0.5
w = 5.545268253 + -0.5

Combine like terms: 5.545268253 + -0.5 = 5.045268253
w = 5.045268253

Simplifying
w = 5.045268253

Subproblem 2
w + 0.5 = -5.545268253

Simplifying
w + 0.5 = -5.545268253

Reorder the terms:
0.5 + w = -5.545268253

Solving
0.5 + w = -5.545268253

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -5.545268253 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -5.545268253 + -0.5
w = -5.545268253 + -0.5

Combine like terms: -5.545268253 + -0.5 = -6.045268253
w = -6.045268253

Simplifying
w = -6.045268253

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.045268253, -6.045268253}
Solution
w = {5.045268253, -6.045268253}