28=(w+2)(w)

Solution for 28=(w+2)(w) equation:

Simplifying
28 = (w + 2)(w)

Reorder the terms:
28 = (2 + w)(w)

Reorder the terms for easier multiplication:
28 = w(2 + w)
28 = (2 * w + w * w)
28 = (2w + w2)

Solving
28 = 2w + w2

Solving for variable 'w'.

Reorder the terms:
28 + -2w + -1w2 = 2w + -2w + w2 + -1w2

Combine like terms: 2w + -2w = 0
28 + -2w + -1w2 = 0 + w2 + -1w2
28 + -2w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
28 + -2w + -1w2 = 0

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

Divide each side by '-1'.
-28 + 2w + w2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 2w + 28 + w2 = 0 + 28

Reorder the terms:
-28 + 28 + 2w + w2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 2w + w2 = 0 + 28
2w + w2 = 0 + 28

Combine like terms: 0 + 28 = 28
2w + w2 = 28

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = 28 + 1

Reorder the terms:
1 + 2w + w2 = 28 + 1

Combine like terms: 28 + 1 = 29
1 + 2w + w2 = 29

Factor a perfect square on the left side:
(w + 1)(w + 1) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(w + 1) equal to 5.385164807 and -5.385164807.

Subproblem 1
w + 1 = 5.385164807

Simplifying
w + 1 = 5.385164807

Reorder the terms:
1 + w = 5.385164807

Solving
1 + w = 5.385164807

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = 5.385164807 + -1

Combine like terms: 1 + -1 = 0
0 + w = 5.385164807 + -1
w = 5.385164807 + -1

Combine like terms: 5.385164807 + -1 = 4.385164807
w = 4.385164807

Simplifying
w = 4.385164807

Subproblem 2
w + 1 = -5.385164807

Simplifying
w + 1 = -5.385164807

Reorder the terms:
1 + w = -5.385164807

Solving
1 + w = -5.385164807

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = -5.385164807 + -1

Combine like terms: 1 + -1 = 0
0 + w = -5.385164807 + -1
w = -5.385164807 + -1

Combine like terms: -5.385164807 + -1 = -6.385164807
w = -6.385164807

Simplifying
w = -6.385164807

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.385164807, -6.385164807}