792=(w*w*2)2+[2(2w+2w)]10

Solution for 792=(w*w*2)2+[2(2w+2w)]10 equation:

Simplifying
792 = (w * w * 2) * 2 + [2(2w + 2w)] * 10

Reorder the terms for easier multiplication:
792 = (2w * w) * 2 + [2(2w + 2w)] * 10

Multiply w * w
792 = (2w2) * 2 + [2(2w + 2w)] * 10

Remove parenthesis around (2w2)
792 = 2w2 * 2 + [2(2w + 2w)] * 10

Reorder the terms for easier multiplication:
792 = 2 * 2w2 + [2(2w + 2w)] * 10

Multiply 2 * 2
792 = 4w2 + [2(2w + 2w)] * 10

Combine like terms: 2w + 2w = 4w
792 = 4w2 + [2(4w)] * 10

Remove parenthesis around (4w)
792 = 4w2 + [2 * 4w] * 10

Multiply 2 * 4
792 = 4w2 + [8w] * 10

Remove brackets around [8w]
792 = 4w2 + 8w * 10

Reorder the terms for easier multiplication:
792 = 4w2 + 8 * 10w

Multiply 8 * 10
792 = 4w2 + 80w

Reorder the terms:
792 = 80w + 4w2

Solving
792 = 80w + 4w2

Solving for variable 'w'.

Reorder the terms:
792 + -80w + -4w2 = 80w + -80w + 4w2 + -4w2

Combine like terms: 80w + -80w = 0
792 + -80w + -4w2 = 0 + 4w2 + -4w2
792 + -80w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
792 + -80w + -4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(198 + -20w + -1w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(198 + -20w + -1w2)' equal to zero and attempt to solve:

Simplifying
198 + -20w + -1w2 = 0

Solving
198 + -20w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-198 + 20w + w2 = 0

Move the constant term to the right:

Add '198' to each side of the equation.
-198 + 20w + 198 + w2 = 0 + 198

Reorder the terms:
-198 + 198 + 20w + w2 = 0 + 198

Combine like terms: -198 + 198 = 0
0 + 20w + w2 = 0 + 198
20w + w2 = 0 + 198

Combine like terms: 0 + 198 = 198
20w + w2 = 198

The w term is 20w.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20w + 100 + w2 = 198 + 100

Reorder the terms:
100 + 20w + w2 = 198 + 100

Combine like terms: 198 + 100 = 298
100 + 20w + w2 = 298

Factor a perfect square on the left side:
(w + 10)(w + 10) = 298

Calculate the square root of the right side: 17.262676502

Break this problem into two subproblems by setting 
(w + 10) equal to 17.262676502 and -17.262676502.

Subproblem 1
w + 10 = 17.262676502

Simplifying
w + 10 = 17.262676502

Reorder the terms:
10 + w = 17.262676502

Solving
10 + w = 17.262676502

Solving for variable 'w'.

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

Add '-10' to each side of the equation.
10 + -10 + w = 17.262676502 + -10

Combine like terms: 10 + -10 = 0
0 + w = 17.262676502 + -10
w = 17.262676502 + -10

Combine like terms: 17.262676502 + -10 = 7.262676502
w = 7.262676502

Simplifying
w = 7.262676502

Subproblem 2
w + 10 = -17.262676502

Simplifying
w + 10 = -17.262676502

Reorder the terms:
10 + w = -17.262676502

Solving
10 + w = -17.262676502

Solving for variable 'w'.

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

Add '-10' to each side of the equation.
10 + -10 + w = -17.262676502 + -10

Combine like terms: 10 + -10 = 0
0 + w = -17.262676502 + -10
w = -17.262676502 + -10

Combine like terms: -17.262676502 + -10 = -27.262676502
w = -27.262676502

Simplifying
w = -27.262676502

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.262676502, -27.262676502}
Solution
w = {7.262676502, -27.262676502}