(w+4)(w+7)=100

Solution for (w+4)(w+7)=100 equation:

Simplifying
(w + 4)(w + 7) = 100

Reorder the terms:
(4 + w)(w + 7) = 100

Reorder the terms:
(4 + w)(7 + w) = 100

Multiply (4 + w) * (7 + w)
(4(7 + w) + w(7 + w)) = 100
((7 * 4 + w * 4) + w(7 + w)) = 100
((28 + 4w) + w(7 + w)) = 100
(28 + 4w + (7 * w + w * w)) = 100
(28 + 4w + (7w + w2)) = 100

Combine like terms: 4w + 7w = 11w
(28 + 11w + w2) = 100

Solving
28 + 11w + w2 = 100

Solving for variable 'w'.

Reorder the terms:
28 + -100 + 11w + w2 = 100 + -100

Combine like terms: 28 + -100 = -72
-72 + 11w + w2 = 100 + -100

Combine like terms: 100 + -100 = 0
-72 + 11w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 11w + 72 + w2 = 0 + 72

Reorder the terms:
-72 + 72 + 11w + w2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 11w + w2 = 0 + 72
11w + w2 = 0 + 72

Combine like terms: 0 + 72 = 72
11w + w2 = 72

The w term is 11w.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11w + 30.25 + w2 = 72 + 30.25

Reorder the terms:
30.25 + 11w + w2 = 72 + 30.25

Combine like terms: 72 + 30.25 = 102.25
30.25 + 11w + w2 = 102.25

Factor a perfect square on the left side:
(w + 5.5)(w + 5.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(w + 5.5) equal to 10.111874208 and -10.111874208.

Subproblem 1
w + 5.5 = 10.111874208

Simplifying
w + 5.5 = 10.111874208

Reorder the terms:
5.5 + w = 10.111874208

Solving
5.5 + w = 10.111874208

Solving for variable 'w'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + w = 10.111874208 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + w = 10.111874208 + -5.5
w = 10.111874208 + -5.5

Combine like terms: 10.111874208 + -5.5 = 4.611874208
w = 4.611874208

Simplifying
w = 4.611874208

Subproblem 2
w + 5.5 = -10.111874208

Simplifying
w + 5.5 = -10.111874208

Reorder the terms:
5.5 + w = -10.111874208

Solving
5.5 + w = -10.111874208

Solving for variable 'w'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + w = -10.111874208 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + w = -10.111874208 + -5.5
w = -10.111874208 + -5.5

Combine like terms: -10.111874208 + -5.5 = -15.611874208
w = -15.611874208

Simplifying
w = -15.611874208

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.611874208, -15.611874208}