7w+2w(w+5)=5

Solution for 7w+2w(w+5)=5 equation:

Simplifying
7w + 2w(w + 5) = 5

Reorder the terms:
7w + 2w(5 + w) = 5
7w + (5 * 2w + w * 2w) = 5
7w + (10w + 2w2) = 5

Combine like terms: 7w + 10w = 17w
17w + 2w2 = 5

Solving
17w + 2w2 = 5

Solving for variable 'w'.

Reorder the terms:
-5 + 17w + 2w2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 17w + 2w2 = 0

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

Divide each side by '2'.
-2.5 + 8.5w + w2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 8.5w + 2.5 + w2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 8.5w + w2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 8.5w + w2 = 0 + 2.5
8.5w + w2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
8.5w + w2 = 2.5

The w term is 8.5w.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5w + 18.0625 + w2 = 2.5 + 18.0625

Reorder the terms:
18.0625 + 8.5w + w2 = 2.5 + 18.0625

Combine like terms: 2.5 + 18.0625 = 20.5625
18.0625 + 8.5w + w2 = 20.5625

Factor a perfect square on the left side:
(w + 4.25)(w + 4.25) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(w + 4.25) equal to 4.534589287 and -4.534589287.

Subproblem 1
w + 4.25 = 4.534589287

Simplifying
w + 4.25 = 4.534589287

Reorder the terms:
4.25 + w = 4.534589287

Solving
4.25 + w = 4.534589287

Solving for variable 'w'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + w = 4.534589287 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + w = 4.534589287 + -4.25
w = 4.534589287 + -4.25

Combine like terms: 4.534589287 + -4.25 = 0.284589287
w = 0.284589287

Simplifying
w = 0.284589287

Subproblem 2
w + 4.25 = -4.534589287

Simplifying
w + 4.25 = -4.534589287

Reorder the terms:
4.25 + w = -4.534589287

Solving
4.25 + w = -4.534589287

Solving for variable 'w'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + w = -4.534589287 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + w = -4.534589287 + -4.25
w = -4.534589287 + -4.25

Combine like terms: -4.534589287 + -4.25 = -8.784589287
w = -8.784589287

Simplifying
w = -8.784589287

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.284589287, -8.784589287}