4w^2+20w+45=0

Solution for 4w^2+20w+45=0 equation:

Simplifying
4w2 + 20w + 45 = 0

Reorder the terms:
45 + 20w + 4w2 = 0

Solving
45 + 20w + 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'.
11.25 + 5w + w2 = 0

Move the constant term to the right:

Add '-11.25' to each side of the equation.
11.25 + 5w + -11.25 + w2 = 0 + -11.25

Reorder the terms:
11.25 + -11.25 + 5w + w2 = 0 + -11.25

Combine like terms: 11.25 + -11.25 = 0.00
0.00 + 5w + w2 = 0 + -11.25
5w + w2 = 0 + -11.25

Combine like terms: 0 + -11.25 = -11.25
5w + w2 = -11.25

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = -11.25 + 6.25

Reorder the terms:
6.25 + 5w + w2 = -11.25 + 6.25

Combine like terms: -11.25 + 6.25 = -5
6.25 + 5w + w2 = -5

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.