72=(w+3)(w+3)

Solution for 72=(w+3)(w+3) equation:

Simplifying
72 = (w + 3)(w + 3)

Reorder the terms:
72 = (3 + w)(w + 3)

Reorder the terms:
72 = (3 + w)(3 + w)

Multiply (3 + w) * (3 + w)
72 = (3(3 + w) + w(3 + w))
72 = ((3 * 3 + w * 3) + w(3 + w))
72 = ((9 + 3w) + w(3 + w))
72 = (9 + 3w + (3 * w + w * w))
72 = (9 + 3w + (3w + w2))

Combine like terms: 3w + 3w = 6w
72 = (9 + 6w + w2)

Solving
72 = 9 + 6w + w2

Solving for variable 'w'.

Combine like terms: 72 + -9 = 63
63 + -6w + -1w2 = 9 + 6w + w2 + -9 + -6w + -1w2

Reorder the terms:
63 + -6w + -1w2 = 9 + -9 + 6w + -6w + w2 + -1w2

Combine like terms: 9 + -9 = 0
63 + -6w + -1w2 = 0 + 6w + -6w + w2 + -1w2
63 + -6w + -1w2 = 6w + -6w + w2 + -1w2

Combine like terms: 6w + -6w = 0
63 + -6w + -1w2 = 0 + w2 + -1w2
63 + -6w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
63 + -6w + -1w2 = 0

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

Divide each side by '-1'.
-63 + 6w + w2 = 0

Move the constant term to the right:

Add '63' to each side of the equation.
-63 + 6w + 63 + w2 = 0 + 63

Reorder the terms:
-63 + 63 + 6w + w2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + 6w + w2 = 0 + 63
6w + w2 = 0 + 63

Combine like terms: 0 + 63 = 63
6w + w2 = 63

The w term is 6w.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6w + 9 + w2 = 63 + 9

Reorder the terms:
9 + 6w + w2 = 63 + 9

Combine like terms: 63 + 9 = 72
9 + 6w + w2 = 72

Factor a perfect square on the left side:
(w + 3)(w + 3) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(w + 3) equal to 8.485281374 and -8.485281374.

Subproblem 1
w + 3 = 8.485281374

Simplifying
w + 3 = 8.485281374

Reorder the terms:
3 + w = 8.485281374

Solving
3 + w = 8.485281374

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + w = 8.485281374 + -3

Combine like terms: 3 + -3 = 0
0 + w = 8.485281374 + -3
w = 8.485281374 + -3

Combine like terms: 8.485281374 + -3 = 5.485281374
w = 5.485281374

Simplifying
w = 5.485281374

Subproblem 2
w + 3 = -8.485281374

Simplifying
w + 3 = -8.485281374

Reorder the terms:
3 + w = -8.485281374

Solving
3 + w = -8.485281374

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + w = -8.485281374 + -3

Combine like terms: 3 + -3 = 0
0 + w = -8.485281374 + -3
w = -8.485281374 + -3

Combine like terms: -8.485281374 + -3 = -11.485281374
w = -11.485281374

Simplifying
w = -11.485281374

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.485281374, -11.485281374}