z^2+9z+54=0

Solution for z^2+9z+54=0 equation:

Simplifying
z2 + 9z + 54 = 0

Reorder the terms:
54 + 9z + z2 = 0

Solving
54 + 9z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + 9z + -54 + z2 = 0 + -54

Reorder the terms:
54 + -54 + 9z + z2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + 9z + z2 = 0 + -54
9z + z2 = 0 + -54

Combine like terms: 0 + -54 = -54
9z + z2 = -54

The z term is 9z.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9z + 20.25 + z2 = -54 + 20.25

Reorder the terms:
20.25 + 9z + z2 = -54 + 20.25

Combine like terms: -54 + 20.25 = -33.75
20.25 + 9z + z2 = -33.75

Factor a perfect square on the left side:
(z + 4.5)(z + 4.5) = -33.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.