2w^2-40w+120=0

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Solution for 2w^2-40w+120=0 equation: 


Simplifying
2w2 + -40w + 120 = 0

Reorder the terms:
120 + -40w + 2w2 = 0

Solving
120 + -40w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(60 + -20w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(60 + -20w + w2)' equal to zero and attempt to solve:

Simplifying
60 + -20w + w2 = 0

Solving
60 + -20w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + -20w + -60 + w2 = 0 + -60

Reorder the terms:
60 + -60 + -20w + w2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -20w + w2 = 0 + -60
-20w + w2 = 0 + -60

Combine like terms: 0 + -60 = -60
-20w + w2 = -60

The w term is -20w.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20w + 100 + w2 = -60 + 100

Reorder the terms:
100 + -20w + w2 = -60 + 100

Combine like terms: -60 + 100 = 40
100 + -20w + w2 = 40

Factor a perfect square on the left side:
(w + -10)(w + -10) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(w + -10) equal to 6.32455532 and -6.32455532.


Subproblem 1
w + -10 = 6.32455532

Simplifying
w + -10 = 6.32455532

Reorder the terms:
-10 + w = 6.32455532

Solving
-10 + w = 6.32455532

Solving for variable 'w'.

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

Add '10' to each side of the equation.
-10 + 10 + w = 6.32455532 + 10

Combine like terms: -10 + 10 = 0
0 + w = 6.32455532 + 10
w = 6.32455532 + 10

Combine like terms: 6.32455532 + 10 = 16.32455532
w = 16.32455532

Simplifying
w = 16.32455532


Subproblem 2
w + -10 = -6.32455532

Simplifying
w + -10 = -6.32455532

Reorder the terms:
-10 + w = -6.32455532

Solving
-10 + w = -6.32455532

Solving for variable 'w'.

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

Add '10' to each side of the equation.
-10 + 10 + w = -6.32455532 + 10

Combine like terms: -10 + 10 = 0
0 + w = -6.32455532 + 10
w = -6.32455532 + 10

Combine like terms: -6.32455532 + 10 = 3.67544468
w = 3.67544468

Simplifying
w = 3.67544468


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {16.32455532, 3.67544468}
Solution
w = {16.32455532, 3.67544468}

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