8w^2+72w-256=0

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Solution for 8w^2+72w-256=0 equation: 


Simplifying
8w2 + 72w + -256 = 0

Reorder the terms:
-256 + 72w + 8w2 = 0

Solving
-256 + 72w + 8w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-32 + 9w + w2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-32 + 9w + w2)' equal to zero and attempt to solve:

Simplifying
-32 + 9w + w2 = 0

Solving
-32 + 9w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 9w + 32 + w2 = 0 + 32

Reorder the terms:
-32 + 32 + 9w + w2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 9w + w2 = 0 + 32
9w + w2 = 0 + 32

Combine like terms: 0 + 32 = 32
9w + w2 = 32

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 = 32 + 20.25

Reorder the terms:
20.25 + 9w + w2 = 32 + 20.25

Combine like terms: 32 + 20.25 = 52.25
20.25 + 9w + w2 = 52.25

Factor a perfect square on the left side:
(w + 4.5)(w + 4.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(w + 4.5) equal to 7.228416147 and -7.228416147.


Subproblem 1
w + 4.5 = 7.228416147

Simplifying
w + 4.5 = 7.228416147

Reorder the terms:
4.5 + w = 7.228416147

Solving
4.5 + w = 7.228416147

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 = 7.228416147 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = 7.228416147 + -4.5
w = 7.228416147 + -4.5

Combine like terms: 7.228416147 + -4.5 = 2.728416147
w = 2.728416147

Simplifying
w = 2.728416147


Subproblem 2
w + 4.5 = -7.228416147

Simplifying
w + 4.5 = -7.228416147

Reorder the terms:
4.5 + w = -7.228416147

Solving
4.5 + w = -7.228416147

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 = -7.228416147 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + w = -7.228416147 + -4.5
w = -7.228416147 + -4.5

Combine like terms: -7.228416147 + -4.5 = -11.728416147
w = -11.728416147

Simplifying
w = -11.728416147


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.728416147, -11.728416147}
Solution
w = {2.728416147, -11.728416147}

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