2w(4+w)+2w=124

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Solution for 2w(4+w)+2w=124 equation: 


Simplifying
2w(4 + w) + 2w = 124
(4 * 2w + w * 2w) + 2w = 124
(8w + 2w2) + 2w = 124

Reorder the terms:
8w + 2w + 2w2 = 124

Combine like terms: 8w + 2w = 10w
10w + 2w2 = 124

Solving
10w + 2w2 = 124

Solving for variable 'w'.

Reorder the terms:
-124 + 10w + 2w2 = 124 + -124

Combine like terms: 124 + -124 = 0
-124 + 10w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-62 + 5w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-62 + 5w + w2)' equal to zero and attempt to solve:

Simplifying
-62 + 5w + w2 = 0

Solving
-62 + 5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + 5w + 62 + w2 = 0 + 62

Reorder the terms:
-62 + 62 + 5w + w2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + 5w + w2 = 0 + 62
5w + w2 = 0 + 62

Combine like terms: 0 + 62 = 62
5w + w2 = 62

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = 62 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 62 + 6.25

Combine like terms: 62 + 6.25 = 68.25
6.25 + 5w + w2 = 68.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 68.25

Calculate the square root of the right side: 8.261355821

Break this problem into two subproblems by setting 
(w + 2.5) equal to 8.261355821 and -8.261355821.


Subproblem 1
w + 2.5 = 8.261355821

Simplifying
w + 2.5 = 8.261355821

Reorder the terms:
2.5 + w = 8.261355821

Solving
2.5 + w = 8.261355821

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = 8.261355821 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 8.261355821 + -2.5
w = 8.261355821 + -2.5

Combine like terms: 8.261355821 + -2.5 = 5.761355821
w = 5.761355821

Simplifying
w = 5.761355821


Subproblem 2
w + 2.5 = -8.261355821

Simplifying
w + 2.5 = -8.261355821

Reorder the terms:
2.5 + w = -8.261355821

Solving
2.5 + w = -8.261355821

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = -8.261355821 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -8.261355821 + -2.5
w = -8.261355821 + -2.5

Combine like terms: -8.261355821 + -2.5 = -10.761355821
w = -10.761355821

Simplifying
w = -10.761355821


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.761355821, -10.761355821}
Solution
w = {5.761355821, -10.761355821}

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