2w(w-7)=72

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Solution for 2w(w-7)=72 equation: 


Simplifying
2w(w + -7) = 72

Reorder the terms:
2w(-7 + w) = 72
(-7 * 2w + w * 2w) = 72
(-14w + 2w2) = 72

Solving
-14w + 2w2 = 72

Solving for variable 'w'.

Reorder the terms:
-72 + -14w + 2w2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + -14w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + -7w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-36 + -7w + w2)' equal to zero and attempt to solve:

Simplifying
-36 + -7w + w2 = 0

Solving
-36 + -7w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -7w + 36 + w2 = 0 + 36

Reorder the terms:
-36 + 36 + -7w + w2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -7w + w2 = 0 + 36
-7w + w2 = 0 + 36

Combine like terms: 0 + 36 = 36
-7w + w2 = 36

The w term is -7w.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7w + 12.25 + w2 = 36 + 12.25

Reorder the terms:
12.25 + -7w + w2 = 36 + 12.25

Combine like terms: 36 + 12.25 = 48.25
12.25 + -7w + w2 = 48.25

Factor a perfect square on the left side:
(w + -3.5)(w + -3.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(w + -3.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
w + -3.5 = 6.946221995

Simplifying
w + -3.5 = 6.946221995

Reorder the terms:
-3.5 + w = 6.946221995

Solving
-3.5 + w = 6.946221995

Solving for variable 'w'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + w = 6.946221995 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + w = 6.946221995 + 3.5
w = 6.946221995 + 3.5

Combine like terms: 6.946221995 + 3.5 = 10.446221995
w = 10.446221995

Simplifying
w = 10.446221995


Subproblem 2
w + -3.5 = -6.946221995

Simplifying
w + -3.5 = -6.946221995

Reorder the terms:
-3.5 + w = -6.946221995

Solving
-3.5 + w = -6.946221995

Solving for variable 'w'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + w = -6.946221995 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + w = -6.946221995 + 3.5
w = -6.946221995 + 3.5

Combine like terms: -6.946221995 + 3.5 = -3.446221995
w = -3.446221995

Simplifying
w = -3.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {10.446221995, -3.446221995}
Solution
w = {10.446221995, -3.446221995}

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