3w^2-6w-108=0

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Solution for 3w^2-6w-108=0 equation: 


Simplifying
3w2 + -6w + -108 = 0

Reorder the terms:
-108 + -6w + 3w2 = 0

Solving
-108 + -6w + 3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-36 + -2w + w2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-36 + -2w + w2)' equal to zero and attempt to solve:

Simplifying
-36 + -2w + w2 = 0

Solving
-36 + -2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -2w + 36 + w2 = 0 + 36

Reorder the terms:
-36 + 36 + -2w + w2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -2w + w2 = 0 + 36
-2w + w2 = 0 + 36

Combine like terms: 0 + 36 = 36
-2w + w2 = 36

The w term is -2w.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2w + 1 + w2 = 36 + 1

Reorder the terms:
1 + -2w + w2 = 36 + 1

Combine like terms: 36 + 1 = 37
1 + -2w + w2 = 37

Factor a perfect square on the left side:
(w + -1)(w + -1) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(w + -1) equal to 6.08276253 and -6.08276253.


Subproblem 1
w + -1 = 6.08276253

Simplifying
w + -1 = 6.08276253

Reorder the terms:
-1 + w = 6.08276253

Solving
-1 + w = 6.08276253

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = 6.08276253 + 1

Combine like terms: -1 + 1 = 0
0 + w = 6.08276253 + 1
w = 6.08276253 + 1

Combine like terms: 6.08276253 + 1 = 7.08276253
w = 7.08276253

Simplifying
w = 7.08276253


Subproblem 2
w + -1 = -6.08276253

Simplifying
w + -1 = -6.08276253

Reorder the terms:
-1 + w = -6.08276253

Solving
-1 + w = -6.08276253

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = -6.08276253 + 1

Combine like terms: -1 + 1 = 0
0 + w = -6.08276253 + 1
w = -6.08276253 + 1

Combine like terms: -6.08276253 + 1 = -5.08276253
w = -5.08276253

Simplifying
w = -5.08276253


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.08276253, -5.08276253}
Solution
w = {7.08276253, -5.08276253}

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