2w^2-18w-4=0

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Solution for 2w^2-18w-4=0 equation: 


Simplifying
2w2 + -18w + -4 = 0

Reorder the terms:
-4 + -18w + 2w2 = 0

Solving
-4 + -18w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -9w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -9w + w2)' equal to zero and attempt to solve:

Simplifying
-2 + -9w + w2 = 0

Solving
-2 + -9w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -9w + 2 + w2 = 0 + 2

Reorder the terms:
-2 + 2 + -9w + w2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -9w + w2 = 0 + 2
-9w + w2 = 0 + 2

Combine like terms: 0 + 2 = 2
-9w + w2 = 2

The w term is -9w.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9w + 20.25 + w2 = 2 + 20.25

Reorder the terms:
20.25 + -9w + w2 = 2 + 20.25

Combine like terms: 2 + 20.25 = 22.25
20.25 + -9w + w2 = 22.25

Factor a perfect square on the left side:
(w + -4.5)(w + -4.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(w + -4.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
w + -4.5 = 4.716990566

Simplifying
w + -4.5 = 4.716990566

Reorder the terms:
-4.5 + w = 4.716990566

Solving
-4.5 + w = 4.716990566

Solving for variable 'w'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + w = 4.716990566 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + w = 4.716990566 + 4.5
w = 4.716990566 + 4.5

Combine like terms: 4.716990566 + 4.5 = 9.216990566
w = 9.216990566

Simplifying
w = 9.216990566


Subproblem 2
w + -4.5 = -4.716990566

Simplifying
w + -4.5 = -4.716990566

Reorder the terms:
-4.5 + w = -4.716990566

Solving
-4.5 + w = -4.716990566

Solving for variable 'w'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + w = -4.716990566 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + w = -4.716990566 + 4.5
w = -4.716990566 + 4.5

Combine like terms: -4.716990566 + 4.5 = -0.216990566
w = -0.216990566

Simplifying
w = -0.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {9.216990566, -0.216990566}
Solution
w = {9.216990566, -0.216990566}

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