4w^2+46w+156=0

Solution for 4w^2+46w+156=0 equation:

Simplifying
4w2 + 46w + 156 = 0

Reorder the terms:
156 + 46w + 4w2 = 0

Solving
156 + 46w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(78 + 23w + 2w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(78 + 23w + 2w2)' equal to zero and attempt to solve:

Simplifying
78 + 23w + 2w2 = 0

Solving
78 + 23w + 2w2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
39 + 11.5w + w2 = 0

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + 11.5w + -39 + w2 = 0 + -39

Reorder the terms:
39 + -39 + 11.5w + w2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + 11.5w + w2 = 0 + -39
11.5w + w2 = 0 + -39

Combine like terms: 0 + -39 = -39
11.5w + w2 = -39

The w term is 11.5w.  Take half its coefficient (5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
11.5w + 33.0625 + w2 = -39 + 33.0625

Reorder the terms:
33.0625 + 11.5w + w2 = -39 + 33.0625

Combine like terms: -39 + 33.0625 = -5.9375
33.0625 + 11.5w + w2 = -5.9375

Factor a perfect square on the left side:
(w + 5.75)(w + 5.75) = -5.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.