4w^2-100w+200=0

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Solution for 4w^2-100w+200=0 equation: 


Simplifying
4w2 + -100w + 200 = 0

Reorder the terms:
200 + -100w + 4w2 = 0

Solving
200 + -100w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(50 + -25w + w2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(50 + -25w + w2)' equal to zero and attempt to solve:

Simplifying
50 + -25w + w2 = 0

Solving
50 + -25w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -25w + -50 + w2 = 0 + -50

Reorder the terms:
50 + -50 + -25w + w2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -25w + w2 = 0 + -50
-25w + w2 = 0 + -50

Combine like terms: 0 + -50 = -50
-25w + w2 = -50

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 = -50 + 156.25

Reorder the terms:
156.25 + -25w + w2 = -50 + 156.25

Combine like terms: -50 + 156.25 = 106.25
156.25 + -25w + w2 = 106.25

Factor a perfect square on the left side:
(w + -12.5)(w + -12.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(w + -12.5) equal to 10.307764064 and -10.307764064.


Subproblem 1
w + -12.5 = 10.307764064

Simplifying
w + -12.5 = 10.307764064

Reorder the terms:
-12.5 + w = 10.307764064

Solving
-12.5 + w = 10.307764064

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 = 10.307764064 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + w = 10.307764064 + 12.5
w = 10.307764064 + 12.5

Combine like terms: 10.307764064 + 12.5 = 22.807764064
w = 22.807764064

Simplifying
w = 22.807764064


Subproblem 2
w + -12.5 = -10.307764064

Simplifying
w + -12.5 = -10.307764064

Reorder the terms:
-12.5 + w = -10.307764064

Solving
-12.5 + w = -10.307764064

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 = -10.307764064 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + w = -10.307764064 + 12.5
w = -10.307764064 + 12.5

Combine like terms: -10.307764064 + 12.5 = 2.192235936
w = 2.192235936

Simplifying
w = 2.192235936


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {22.807764064, 2.192235936}
Solution
w = {22.807764064, 2.192235936}

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