2(w+9)2w=72

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Solution for 2(w+9)2w=72 equation: 


Simplifying
2(w + 9) * 2w = 72

Reorder the terms:
2(9 + w) * 2w = 72

Reorder the terms for easier multiplication:
2 * 2w(9 + w) = 72

Multiply 2 * 2
4w(9 + w) = 72
(9 * 4w + w * 4w) = 72
(36w + 4w2) = 72

Solving
36w + 4w2 = 72

Solving for variable 'w'.

Reorder the terms:
-72 + 36w + 4w2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 36w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 9w + w2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-18 + 9w + w2)' equal to zero and attempt to solve:

Simplifying
-18 + 9w + w2 = 0

Solving
-18 + 9w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 9w + 18 + w2 = 0 + 18

Reorder the terms:
-18 + 18 + 9w + w2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 9w + w2 = 0 + 18
9w + w2 = 0 + 18

Combine like terms: 0 + 18 = 18
9w + w2 = 18

The w term is 9w.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9w + 20.25 + w2 = 18 + 20.25

Reorder the terms:
20.25 + 9w + w2 = 18 + 20.25

Combine like terms: 18 + 20.25 = 38.25
20.25 + 9w + w2 = 38.25

Factor a perfect square on the left side:
(w + 4.5)(w + 4.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(w + 4.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
w + 4.5 = 6.184658438

Simplifying
w + 4.5 = 6.184658438

Reorder the terms:
4.5 + w = 6.184658438

Solving
4.5 + w = 6.184658438

Solving for variable 'w'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + w = 6.184658438 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = 6.184658438 + -4.5
w = 6.184658438 + -4.5

Combine like terms: 6.184658438 + -4.5 = 1.684658438
w = 1.684658438

Simplifying
w = 1.684658438


Subproblem 2
w + 4.5 = -6.184658438

Simplifying
w + 4.5 = -6.184658438

Reorder the terms:
4.5 + w = -6.184658438

Solving
4.5 + w = -6.184658438

Solving for variable 'w'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + w = -6.184658438 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = -6.184658438 + -4.5
w = -6.184658438 + -4.5

Combine like terms: -6.184658438 + -4.5 = -10.684658438
w = -10.684658438

Simplifying
w = -10.684658438


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.684658438, -10.684658438}
Solution
w = {1.684658438, -10.684658438}

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