-2(w^2-25w+125)=0

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Solution for -2(w^2-25w+125)=0 equation: 


Simplifying
-2(w2 + -25w + 125) = 0

Reorder the terms:
-2(125 + -25w + w2) = 0
(125 * -2 + -25w * -2 + w2 * -2) = 0
(-250 + 50w + -2w2) = 0

Solving
-250 + 50w + -2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + 25w + -1w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-125 + 25w + -1w2)' equal to zero and attempt to solve:

Simplifying
-125 + 25w + -1w2 = 0

Solving
-125 + 25w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
125 + -25w + w2 = 0

Move the constant term to the right:

Add '-125' to each side of the equation.
125 + -25w + -125 + w2 = 0 + -125

Reorder the terms:
125 + -125 + -25w + w2 = 0 + -125

Combine like terms: 125 + -125 = 0
0 + -25w + w2 = 0 + -125
-25w + w2 = 0 + -125

Combine like terms: 0 + -125 = -125
-25w + w2 = -125

The w term is -25w.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25w + 156.25 + w2 = -125 + 156.25

Reorder the terms:
156.25 + -25w + w2 = -125 + 156.25

Combine like terms: -125 + 156.25 = 31.25
156.25 + -25w + w2 = 31.25

Factor a perfect square on the left side:
(w + -12.5)(w + -12.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(w + -12.5) equal to 5.590169944 and -5.590169944.


Subproblem 1
w + -12.5 = 5.590169944

Simplifying
w + -12.5 = 5.590169944

Reorder the terms:
-12.5 + w = 5.590169944

Solving
-12.5 + w = 5.590169944

Solving for variable 'w'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + w = 5.590169944 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + w = 5.590169944 + 12.5
w = 5.590169944 + 12.5

Combine like terms: 5.590169944 + 12.5 = 18.090169944
w = 18.090169944

Simplifying
w = 18.090169944


Subproblem 2
w + -12.5 = -5.590169944

Simplifying
w + -12.5 = -5.590169944

Reorder the terms:
-12.5 + w = -5.590169944

Solving
-12.5 + w = -5.590169944

Solving for variable 'w'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + w = -5.590169944 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + w = -5.590169944 + 12.5
w = -5.590169944 + 12.5

Combine like terms: -5.590169944 + 12.5 = 6.909830056
w = 6.909830056

Simplifying
w = 6.909830056


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {18.090169944, 6.909830056}
Solution
w = {18.090169944, 6.909830056}

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