2w^2+4w-66=0

Solution for 2w^2+4w-66=0 equation:

Simplifying
2w2 + 4w + -66 = 0

Reorder the terms:
-66 + 4w + 2w2 = 0

Solving
-66 + 4w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + 2w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-33 + 2w + w2)' equal to zero and attempt to solve:

Simplifying
-33 + 2w + w2 = 0

Solving
-33 + 2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + 2w + 33 + w2 = 0 + 33

Reorder the terms:
-33 + 33 + 2w + w2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + 2w + w2 = 0 + 33
2w + w2 = 0 + 33

Combine like terms: 0 + 33 = 33
2w + w2 = 33

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 = 33 + 1

Reorder the terms:
1 + 2w + w2 = 33 + 1

Combine like terms: 33 + 1 = 34
1 + 2w + w2 = 34

Factor a perfect square on the left side:
(w + 1)(w + 1) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(w + 1) equal to 5.830951895 and -5.830951895.

Subproblem 1
w + 1 = 5.830951895

Simplifying
w + 1 = 5.830951895

Reorder the terms:
1 + w = 5.830951895

Solving
1 + w = 5.830951895

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 = 5.830951895 + -1

Combine like terms: 1 + -1 = 0
0 + w = 5.830951895 + -1
w = 5.830951895 + -1

Combine like terms: 5.830951895 + -1 = 4.830951895
w = 4.830951895

Simplifying
w = 4.830951895

Subproblem 2
w + 1 = -5.830951895

Simplifying
w + 1 = -5.830951895

Reorder the terms:
1 + w = -5.830951895

Solving
1 + w = -5.830951895

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 = -5.830951895 + -1

Combine like terms: 1 + -1 = 0
0 + w = -5.830951895 + -1
w = -5.830951895 + -1

Combine like terms: -5.830951895 + -1 = -6.830951895
w = -6.830951895

Simplifying
w = -6.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.830951895, -6.830951895}
Solution
w = {4.830951895, -6.830951895}