w^2-6w-4=0

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Solution for w^2-6w-4=0 equation: 


Simplifying
w2 + -6w + -4 = 0

Reorder the terms:
-4 + -6w + w2 = 0

Solving
-4 + -6w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -6w + 4 + w2 = 0 + 4

Reorder the terms:
-4 + 4 + -6w + w2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -6w + w2 = 0 + 4
-6w + w2 = 0 + 4

Combine like terms: 0 + 4 = 4
-6w + w2 = 4

The w term is -6w.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6w + 9 + w2 = 4 + 9

Reorder the terms:
9 + -6w + w2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + -6w + w2 = 13

Factor a perfect square on the left side:
(w + -3)(w + -3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(w + -3) equal to 3.605551275 and -3.605551275.


Subproblem 1
w + -3 = 3.605551275

Simplifying
w + -3 = 3.605551275

Reorder the terms:
-3 + w = 3.605551275

Solving
-3 + w = 3.605551275

Solving for variable 'w'.

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

Add '3' to each side of the equation.
-3 + 3 + w = 3.605551275 + 3

Combine like terms: -3 + 3 = 0
0 + w = 3.605551275 + 3
w = 3.605551275 + 3

Combine like terms: 3.605551275 + 3 = 6.605551275
w = 6.605551275

Simplifying
w = 6.605551275


Subproblem 2
w + -3 = -3.605551275

Simplifying
w + -3 = -3.605551275

Reorder the terms:
-3 + w = -3.605551275

Solving
-3 + w = -3.605551275

Solving for variable 'w'.

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

Add '3' to each side of the equation.
-3 + 3 + w = -3.605551275 + 3

Combine like terms: -3 + 3 = 0
0 + w = -3.605551275 + 3
w = -3.605551275 + 3

Combine like terms: -3.605551275 + 3 = -0.605551275
w = -0.605551275

Simplifying
w = -0.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.605551275, -0.605551275}

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