2w^2-8w-200=0

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Solution for 2w^2-8w-200=0 equation: 


Simplifying
2w2 + -8w + -200 = 0

Reorder the terms:
-200 + -8w + 2w2 = 0

Solving
-200 + -8w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-100 + -4w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-100 + -4w + w2)' equal to zero and attempt to solve:

Simplifying
-100 + -4w + w2 = 0

Solving
-100 + -4w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -4w + 100 + w2 = 0 + 100

Reorder the terms:
-100 + 100 + -4w + w2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -4w + w2 = 0 + 100
-4w + w2 = 0 + 100

Combine like terms: 0 + 100 = 100
-4w + w2 = 100

The w term is -4w.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4w + 4 + w2 = 100 + 4

Reorder the terms:
4 + -4w + w2 = 100 + 4

Combine like terms: 100 + 4 = 104
4 + -4w + w2 = 104

Factor a perfect square on the left side:
(w + -2)(w + -2) = 104

Calculate the square root of the right side: 10.198039027

Break this problem into two subproblems by setting 
(w + -2) equal to 10.198039027 and -10.198039027.


Subproblem 1
w + -2 = 10.198039027

Simplifying
w + -2 = 10.198039027

Reorder the terms:
-2 + w = 10.198039027

Solving
-2 + w = 10.198039027

Solving for variable 'w'.

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

Add '2' to each side of the equation.
-2 + 2 + w = 10.198039027 + 2

Combine like terms: -2 + 2 = 0
0 + w = 10.198039027 + 2
w = 10.198039027 + 2

Combine like terms: 10.198039027 + 2 = 12.198039027
w = 12.198039027

Simplifying
w = 12.198039027


Subproblem 2
w + -2 = -10.198039027

Simplifying
w + -2 = -10.198039027

Reorder the terms:
-2 + w = -10.198039027

Solving
-2 + w = -10.198039027

Solving for variable 'w'.

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

Add '2' to each side of the equation.
-2 + 2 + w = -10.198039027 + 2

Combine like terms: -2 + 2 = 0
0 + w = -10.198039027 + 2
w = -10.198039027 + 2

Combine like terms: -10.198039027 + 2 = -8.198039027
w = -8.198039027

Simplifying
w = -8.198039027


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {12.198039027, -8.198039027}
Solution
w = {12.198039027, -8.198039027}

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