5z^2+10z+9=0

Solution for 5z^2+10z+9=0 equation:

Simplifying
5z2 + 10z + 9 = 0

Reorder the terms:
9 + 10z + 5z2 = 0

Solving
9 + 10z + 5z2 = 0

Solving for variable 'z'.

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

Divide each side by '5'.
1.8 + 2z + z2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + 2z + -1.8 + z2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + 2z + z2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + 2z + z2 = 0 + -1.8
2z + z2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
2z + z2 = -1.8

The z term is 2z.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2z + 1 + z2 = -1.8 + 1

Reorder the terms:
1 + 2z + z2 = -1.8 + 1

Combine like terms: -1.8 + 1 = -0.8
1 + 2z + z2 = -0.8

Factor a perfect square on the left side:
(z + 1)(z + 1) = -0.8

Can't calculate square root of the right side.

The solution to this equation could not be determined.