4w^2+8w+9=0

Solution for 4w^2+8w+9=0 equation:

Simplifying
4w2 + 8w + 9 = 0

Reorder the terms:
9 + 8w + 4w2 = 0

Solving
9 + 8w + 4w2 = 0

Solving for variable 'w'.

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

Divide each side by '4'.
2.25 + 2w + w2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + 2w + -2.25 + w2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + 2w + w2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + 2w + w2 = 0 + -2.25
2w + w2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
2w + w2 = -2.25

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 = -2.25 + 1

Reorder the terms:
1 + 2w + w2 = -2.25 + 1

Combine like terms: -2.25 + 1 = -1.25
1 + 2w + w2 = -1.25

Factor a perfect square on the left side:
(w + 1)(w + 1) = -1.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.