w*w-16w-256=0

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Solution for w*w-16w-256=0 equation: 


Simplifying
w * w + -16w + -256 = 0

Multiply w * w
w2 + -16w + -256 = 0

Reorder the terms:
-256 + -16w + w2 = 0

Solving
-256 + -16w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '256' to each side of the equation.
-256 + -16w + 256 + w2 = 0 + 256

Reorder the terms:
-256 + 256 + -16w + w2 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + -16w + w2 = 0 + 256
-16w + w2 = 0 + 256

Combine like terms: 0 + 256 = 256
-16w + w2 = 256

The w term is -16w.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16w + 64 + w2 = 256 + 64

Reorder the terms:
64 + -16w + w2 = 256 + 64

Combine like terms: 256 + 64 = 320
64 + -16w + w2 = 320

Factor a perfect square on the left side:
(w + -8)(w + -8) = 320

Calculate the square root of the right side: 17.88854382

Break this problem into two subproblems by setting 
(w + -8) equal to 17.88854382 and -17.88854382.


Subproblem 1
w + -8 = 17.88854382

Simplifying
w + -8 = 17.88854382

Reorder the terms:
-8 + w = 17.88854382

Solving
-8 + w = 17.88854382

Solving for variable 'w'.

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

Add '8' to each side of the equation.
-8 + 8 + w = 17.88854382 + 8

Combine like terms: -8 + 8 = 0
0 + w = 17.88854382 + 8
w = 17.88854382 + 8

Combine like terms: 17.88854382 + 8 = 25.88854382
w = 25.88854382

Simplifying
w = 25.88854382


Subproblem 2
w + -8 = -17.88854382

Simplifying
w + -8 = -17.88854382

Reorder the terms:
-8 + w = -17.88854382

Solving
-8 + w = -17.88854382

Solving for variable 'w'.

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

Add '8' to each side of the equation.
-8 + 8 + w = -17.88854382 + 8

Combine like terms: -8 + 8 = 0
0 + w = -17.88854382 + 8
w = -17.88854382 + 8

Combine like terms: -17.88854382 + 8 = -9.88854382
w = -9.88854382

Simplifying
w = -9.88854382


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {25.88854382, -9.88854382}

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