(5+2w)w=34

Solution for (5+2w)w=34 equation:

Simplifying
(5 + 2w) * w = 34

Reorder the terms for easier multiplication:
w(5 + 2w) = 34
(5 * w + 2w * w) = 34
(5w + 2w2) = 34

Solving
5w + 2w2 = 34

Solving for variable 'w'.

Reorder the terms:
-34 + 5w + 2w2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + 5w + 2w2 = 0

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

Divide each side by '2'.
-17 + 2.5w + w2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 2.5w + 17 + w2 = 0 + 17

Reorder the terms:
-17 + 17 + 2.5w + w2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 2.5w + w2 = 0 + 17
2.5w + w2 = 0 + 17

Combine like terms: 0 + 17 = 17
2.5w + w2 = 17

The w term is 2.5w.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5w + 1.5625 + w2 = 17 + 1.5625

Reorder the terms:
1.5625 + 2.5w + w2 = 17 + 1.5625

Combine like terms: 17 + 1.5625 = 18.5625
1.5625 + 2.5w + w2 = 18.5625

Factor a perfect square on the left side:
(w + 1.25)(w + 1.25) = 18.5625

Calculate the square root of the right side: 4.308421985

Break this problem into two subproblems by setting 
(w + 1.25) equal to 4.308421985 and -4.308421985.

Subproblem 1
w + 1.25 = 4.308421985

Simplifying
w + 1.25 = 4.308421985

Reorder the terms:
1.25 + w = 4.308421985

Solving
1.25 + w = 4.308421985

Solving for variable 'w'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + w = 4.308421985 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + w = 4.308421985 + -1.25
w = 4.308421985 + -1.25

Combine like terms: 4.308421985 + -1.25 = 3.058421985
w = 3.058421985

Simplifying
w = 3.058421985

Subproblem 2
w + 1.25 = -4.308421985

Simplifying
w + 1.25 = -4.308421985

Reorder the terms:
1.25 + w = -4.308421985

Solving
1.25 + w = -4.308421985

Solving for variable 'w'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + w = -4.308421985 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + w = -4.308421985 + -1.25
w = -4.308421985 + -1.25

Combine like terms: -4.308421985 + -1.25 = -5.558421985
w = -5.558421985

Simplifying
w = -5.558421985

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.058421985, -5.558421985}