z^2+3z+9=0

Solution for z^2+3z+9=0 equation:

Simplifying
z2 + 3z + 9 = 0

Reorder the terms:
9 + 3z + z2 = 0

Solving
9 + 3z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 3z + -9 + z2 = 0 + -9

Reorder the terms:
9 + -9 + 3z + z2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 3z + z2 = 0 + -9
3z + z2 = 0 + -9

Combine like terms: 0 + -9 = -9
3z + z2 = -9

The z term is 3z.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3z + 2.25 + z2 = -9 + 2.25

Reorder the terms:
2.25 + 3z + z2 = -9 + 2.25

Combine like terms: -9 + 2.25 = -6.75
2.25 + 3z + z2 = -6.75

Factor a perfect square on the left side:
(z + 1.5)(z + 1.5) = -6.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.