2z^2+8z+9=0

Solution for 2z^2+8z+9=0 equation:

Simplifying
2z2 + 8z + 9 = 0

Reorder the terms:
9 + 8z + 2z2 = 0

Solving
9 + 8z + 2z2 = 0

Solving for variable 'z'.

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

Divide each side by '2'.
4.5 + 4z + z2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 4z + -4.5 + z2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 4z + z2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 4z + z2 = 0 + -4.5
4z + z2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
4z + z2 = -4.5

The z term is 4z.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4z + 4 + z2 = -4.5 + 4

Reorder the terms:
4 + 4z + z2 = -4.5 + 4

Combine like terms: -4.5 + 4 = -0.5
4 + 4z + z2 = -0.5

Factor a perfect square on the left side:
(z + 2)(z + 2) = -0.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.