w^2+2w+19=0

Solution for w^2+2w+19=0 equation:

Simplifying
w2 + 2w + 19 = 0

Reorder the terms:
19 + 2w + w2 = 0

Solving
19 + 2w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + 2w + -19 + w2 = 0 + -19

Reorder the terms:
19 + -19 + 2w + w2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 2w + w2 = 0 + -19
2w + w2 = 0 + -19

Combine like terms: 0 + -19 = -19
2w + w2 = -19

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 = -19 + 1

Reorder the terms:
1 + 2w + w2 = -19 + 1

Combine like terms: -19 + 1 = -18
1 + 2w + w2 = -18

Factor a perfect square on the left side:
(w + 1)(w + 1) = -18

Can't calculate square root of the right side.

The solution to this equation could not be determined.