2w^2+13w+42=0

Solution for 2w^2+13w+42=0 equation:

Simplifying
2w2 + 13w + 42 = 0

Reorder the terms:
42 + 13w + 2w2 = 0

Solving
42 + 13w + 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'.
21 + 6.5w + w2 = 0

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 6.5w + -21 + w2 = 0 + -21

Reorder the terms:
21 + -21 + 6.5w + w2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 6.5w + w2 = 0 + -21
6.5w + w2 = 0 + -21

Combine like terms: 0 + -21 = -21
6.5w + w2 = -21

The w term is 6.5w.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5w + 10.5625 + w2 = -21 + 10.5625

Reorder the terms:
10.5625 + 6.5w + w2 = -21 + 10.5625

Combine like terms: -21 + 10.5625 = -10.4375
10.5625 + 6.5w + w2 = -10.4375

Factor a perfect square on the left side:
(w + 3.25)(w + 3.25) = -10.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.