5z^2+9z+11=0

Solution for 5z^2+9z+11=0 equation:

Simplifying
5z2 + 9z + 11 = 0

Reorder the terms:
11 + 9z + 5z2 = 0

Solving
11 + 9z + 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'.
2.2 + 1.8z + z2 = 0

Move the constant term to the right:

Add '-2.2' to each side of the equation.
2.2 + 1.8z + -2.2 + z2 = 0 + -2.2

Reorder the terms:
2.2 + -2.2 + 1.8z + z2 = 0 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + 1.8z + z2 = 0 + -2.2
1.8z + z2 = 0 + -2.2

Combine like terms: 0 + -2.2 = -2.2
1.8z + z2 = -2.2

The z term is 1.8z.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8z + 0.81 + z2 = -2.2 + 0.81

Reorder the terms:
0.81 + 1.8z + z2 = -2.2 + 0.81

Combine like terms: -2.2 + 0.81 = -1.39
0.81 + 1.8z + z2 = -1.39

Factor a perfect square on the left side:
(z + 0.9)(z + 0.9) = -1.39

Can't calculate square root of the right side.

The solution to this equation could not be determined.