224=(w+12)w

Solution for 224=(w+12)w equation:

Simplifying
224 = (w + 12) * w

Reorder the terms:
224 = (12 + w) * w

Reorder the terms for easier multiplication:
224 = w(12 + w)
224 = (12 * w + w * w)
224 = (12w + w2)

Solving
224 = 12w + w2

Solving for variable 'w'.

Reorder the terms:
224 + -12w + -1w2 = 12w + -12w + w2 + -1w2

Combine like terms: 12w + -12w = 0
224 + -12w + -1w2 = 0 + w2 + -1w2
224 + -12w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
224 + -12w + -1w2 = 0

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

Divide each side by '-1'.
-224 + 12w + w2 = 0

Move the constant term to the right:

Add '224' to each side of the equation.
-224 + 12w + 224 + w2 = 0 + 224

Reorder the terms:
-224 + 224 + 12w + w2 = 0 + 224

Combine like terms: -224 + 224 = 0
0 + 12w + w2 = 0 + 224
12w + w2 = 0 + 224

Combine like terms: 0 + 224 = 224
12w + w2 = 224

The w term is 12w.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12w + 36 + w2 = 224 + 36

Reorder the terms:
36 + 12w + w2 = 224 + 36

Combine like terms: 224 + 36 = 260
36 + 12w + w2 = 260

Factor a perfect square on the left side:
(w + 6)(w + 6) = 260

Calculate the square root of the right side: 16.124515497

Break this problem into two subproblems by setting 
(w + 6) equal to 16.124515497 and -16.124515497.

Subproblem 1
w + 6 = 16.124515497

Simplifying
w + 6 = 16.124515497

Reorder the terms:
6 + w = 16.124515497

Solving
6 + w = 16.124515497

Solving for variable 'w'.

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

Add '-6' to each side of the equation.
6 + -6 + w = 16.124515497 + -6

Combine like terms: 6 + -6 = 0
0 + w = 16.124515497 + -6
w = 16.124515497 + -6

Combine like terms: 16.124515497 + -6 = 10.124515497
w = 10.124515497

Simplifying
w = 10.124515497

Subproblem 2
w + 6 = -16.124515497

Simplifying
w + 6 = -16.124515497

Reorder the terms:
6 + w = -16.124515497

Solving
6 + w = -16.124515497

Solving for variable 'w'.

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

Add '-6' to each side of the equation.
6 + -6 + w = -16.124515497 + -6

Combine like terms: 6 + -6 = 0
0 + w = -16.124515497 + -6
w = -16.124515497 + -6

Combine like terms: -16.124515497 + -6 = -22.124515497
w = -22.124515497

Simplifying
w = -22.124515497

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {10.124515497, -22.124515497}