2z^2+4z+9=0

Solution for 2z^2+4z+9=0 equation:

Simplifying
2z2 + 4z + 9 = 0

Reorder the terms:
9 + 4z + 2z2 = 0

Solving
9 + 4z + 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 + 2z + z2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 2z + -4.5 + z2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 2z + z2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 2z + z2 = 0 + -4.5
2z + z2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
2z + z2 = -4.5

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 = -4.5 + 1

Reorder the terms:
1 + 2z + z2 = -4.5 + 1

Combine like terms: -4.5 + 1 = -3.5
1 + 2z + z2 = -3.5

Factor a perfect square on the left side:
(z + 1)(z + 1) = -3.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.