6w^2-24w-24=0

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Solution for 6w^2-24w-24=0 equation: 


Simplifying
6w2 + -24w + -24 = 0

Reorder the terms:
-24 + -24w + 6w2 = 0

Solving
-24 + -24w + 6w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + -4w + w2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-4 + -4w + w2)' equal to zero and attempt to solve:

Simplifying
-4 + -4w + w2 = 0

Solving
-4 + -4w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -4w + 4 + w2 = 0 + 4

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

Combine like terms: -4 + 4 = 0
0 + -4w + w2 = 0 + 4
-4w + w2 = 0 + 4

Combine like terms: 0 + 4 = 4
-4w + w2 = 4

The w term is -4w.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4w + 4 + w2 = 4 + 4

Reorder the terms:
4 + -4w + w2 = 4 + 4

Combine like terms: 4 + 4 = 8
4 + -4w + w2 = 8

Factor a perfect square on the left side:
(w + -2)(w + -2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(w + -2) equal to 2.828427125 and -2.828427125.


Subproblem 1
w + -2 = 2.828427125

Simplifying
w + -2 = 2.828427125

Reorder the terms:
-2 + w = 2.828427125

Solving
-2 + w = 2.828427125

Solving for variable 'w'.

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

Add '2' to each side of the equation.
-2 + 2 + w = 2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + w = 2.828427125 + 2
w = 2.828427125 + 2

Combine like terms: 2.828427125 + 2 = 4.828427125
w = 4.828427125

Simplifying
w = 4.828427125


Subproblem 2
w + -2 = -2.828427125

Simplifying
w + -2 = -2.828427125

Reorder the terms:
-2 + w = -2.828427125

Solving
-2 + w = -2.828427125

Solving for variable 'w'.

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

Add '2' to each side of the equation.
-2 + 2 + w = -2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + w = -2.828427125 + 2
w = -2.828427125 + 2

Combine like terms: -2.828427125 + 2 = -0.828427125
w = -0.828427125

Simplifying
w = -0.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.828427125, -0.828427125}
Solution
w = {4.828427125, -0.828427125}

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