2(2w+5)2w=46

Solution for 2(2w+5)2w=46 equation:

Simplifying
2(2w + 5) * 2w = 46

Reorder the terms:
2(5 + 2w) * 2w = 46

Reorder the terms for easier multiplication:
2 * 2w(5 + 2w) = 46

Multiply 2 * 2
4w(5 + 2w) = 46
(5 * 4w + 2w * 4w) = 46
(20w + 8w2) = 46

Solving
20w + 8w2 = 46

Solving for variable 'w'.

Reorder the terms:
-46 + 20w + 8w2 = 46 + -46

Combine like terms: 46 + -46 = 0
-46 + 20w + 8w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-23 + 10w + 4w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-23 + 10w + 4w2)' equal to zero and attempt to solve:

Simplifying
-23 + 10w + 4w2 = 0

Solving
-23 + 10w + 4w2 = 0

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

Divide each side by '4'.
-5.75 + 2.5w + w2 = 0

Move the constant term to the right:

Add '5.75' to each side of the equation.
-5.75 + 2.5w + 5.75 + w2 = 0 + 5.75

Reorder the terms:
-5.75 + 5.75 + 2.5w + w2 = 0 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + 2.5w + w2 = 0 + 5.75
2.5w + w2 = 0 + 5.75

Combine like terms: 0 + 5.75 = 5.75
2.5w + w2 = 5.75

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 = 5.75 + 1.5625

Reorder the terms:
1.5625 + 2.5w + w2 = 5.75 + 1.5625

Combine like terms: 5.75 + 1.5625 = 7.3125
1.5625 + 2.5w + w2 = 7.3125

Factor a perfect square on the left side:
(w + 1.25)(w + 1.25) = 7.3125

Calculate the square root of the right side: 2.704163457

Break this problem into two subproblems by setting 
(w + 1.25) equal to 2.704163457 and -2.704163457.

Subproblem 1
w + 1.25 = 2.704163457

Simplifying
w + 1.25 = 2.704163457

Reorder the terms:
1.25 + w = 2.704163457

Solving
1.25 + w = 2.704163457

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 = 2.704163457 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + w = 2.704163457 + -1.25
w = 2.704163457 + -1.25

Combine like terms: 2.704163457 + -1.25 = 1.454163457
w = 1.454163457

Simplifying
w = 1.454163457

Subproblem 2
w + 1.25 = -2.704163457

Simplifying
w + 1.25 = -2.704163457

Reorder the terms:
1.25 + w = -2.704163457

Solving
1.25 + w = -2.704163457

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 = -2.704163457 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + w = -2.704163457 + -1.25
w = -2.704163457 + -1.25

Combine like terms: -2.704163457 + -1.25 = -3.954163457
w = -3.954163457

Simplifying
w = -3.954163457

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.454163457, -3.954163457}
Solution
w = {1.454163457, -3.954163457}