2w^2+10w+37=0

Solution for 2w^2+10w+37=0 equation:

Simplifying
2w2 + 10w + 37 = 0

Reorder the terms:
37 + 10w + 2w2 = 0

Solving
37 + 10w + 2w2 = 0

Solving for variable 'w'.

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

Divide each side by '2'.
18.5 + 5w + w2 = 0

Move the constant term to the right:

Add '-18.5' to each side of the equation.
18.5 + 5w + -18.5 + w2 = 0 + -18.5

Reorder the terms:
18.5 + -18.5 + 5w + w2 = 0 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + 5w + w2 = 0 + -18.5
5w + w2 = 0 + -18.5

Combine like terms: 0 + -18.5 = -18.5
5w + w2 = -18.5

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = -18.5 + 6.25

Reorder the terms:
6.25 + 5w + w2 = -18.5 + 6.25

Combine like terms: -18.5 + 6.25 = -12.25
6.25 + 5w + w2 = -12.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = -12.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.