2w^2+126w+240=0

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Solution for 2w^2+126w+240=0 equation: 


Simplifying
2w2 + 126w + 240 = 0

Reorder the terms:
240 + 126w + 2w2 = 0

Solving
240 + 126w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(120 + 63w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(120 + 63w + w2)' equal to zero and attempt to solve:

Simplifying
120 + 63w + w2 = 0

Solving
120 + 63w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-120' to each side of the equation.
120 + 63w + -120 + w2 = 0 + -120

Reorder the terms:
120 + -120 + 63w + w2 = 0 + -120

Combine like terms: 120 + -120 = 0
0 + 63w + w2 = 0 + -120
63w + w2 = 0 + -120

Combine like terms: 0 + -120 = -120
63w + w2 = -120

The w term is 63w.  Take half its coefficient (31.5).
Square it (992.25) and add it to both sides.

Add '992.25' to each side of the equation.
63w + 992.25 + w2 = -120 + 992.25

Reorder the terms:
992.25 + 63w + w2 = -120 + 992.25

Combine like terms: -120 + 992.25 = 872.25
992.25 + 63w + w2 = 872.25

Factor a perfect square on the left side:
(w + 31.5)(w + 31.5) = 872.25

Calculate the square root of the right side: 29.533878851

Break this problem into two subproblems by setting 
(w + 31.5) equal to 29.533878851 and -29.533878851.


Subproblem 1
w + 31.5 = 29.533878851

Simplifying
w + 31.5 = 29.533878851

Reorder the terms:
31.5 + w = 29.533878851

Solving
31.5 + w = 29.533878851

Solving for variable 'w'.

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

Add '-31.5' to each side of the equation.
31.5 + -31.5 + w = 29.533878851 + -31.5

Combine like terms: 31.5 + -31.5 = 0.0
0.0 + w = 29.533878851 + -31.5
w = 29.533878851 + -31.5

Combine like terms: 29.533878851 + -31.5 = -1.966121149
w = -1.966121149

Simplifying
w = -1.966121149


Subproblem 2
w + 31.5 = -29.533878851

Simplifying
w + 31.5 = -29.533878851

Reorder the terms:
31.5 + w = -29.533878851

Solving
31.5 + w = -29.533878851

Solving for variable 'w'.

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

Add '-31.5' to each side of the equation.
31.5 + -31.5 + w = -29.533878851 + -31.5

Combine like terms: 31.5 + -31.5 = 0.0
0.0 + w = -29.533878851 + -31.5
w = -29.533878851 + -31.5

Combine like terms: -29.533878851 + -31.5 = -61.033878851
w = -61.033878851

Simplifying
w = -61.033878851


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-1.966121149, -61.033878851}
Solution
w = {-1.966121149, -61.033878851}

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