5w^2+1w+1=0

Solution for 5w^2+1w+1=0 equation:

Simplifying
5w2 + 1w + 1 = 0

Reorder the terms:
1 + 1w + 5w2 = 0

Solving
1 + 1w + 5w2 = 0

Solving for variable 'w'.

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

Divide each side by '5'.
0.2 + 0.2w + w2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 0.2w + -0.2 + w2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 0.2w + w2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 0.2w + w2 = 0 + -0.2
0.2w + w2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
0.2w + w2 = -0.2

The w term is 0.2w.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2w + 0.01 + w2 = -0.2 + 0.01

Reorder the terms:
0.01 + 0.2w + w2 = -0.2 + 0.01

Combine like terms: -0.2 + 0.01 = -0.19
0.01 + 0.2w + w2 = -0.19

Factor a perfect square on the left side:
(w + 0.1)(w + 0.1) = -0.19

Can't calculate square root of the right side.

The solution to this equation could not be determined.