2w^2+6w+9=0

Solution for 2w^2+6w+9=0 equation:

Simplifying
2w2 + 6w + 9 = 0

Reorder the terms:
9 + 6w + 2w2 = 0

Solving
9 + 6w + 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'.
4.5 + 3w + w2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 3w + -4.5 + w2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 3w + w2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 3w + w2 = 0 + -4.5
3w + w2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
3w + w2 = -4.5

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = -4.5 + 2.25

Reorder the terms:
2.25 + 3w + w2 = -4.5 + 2.25

Combine like terms: -4.5 + 2.25 = -2.25
2.25 + 3w + w2 = -2.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.