z^2+3z+4=0

Solution for z^2+3z+4=0 equation:

Simplifying
z2 + 3z + 4 = 0

Reorder the terms:
4 + 3z + z2 = 0

Solving
4 + 3z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 3z + -4 + z2 = 0 + -4

Reorder the terms:
4 + -4 + 3z + z2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3z + z2 = 0 + -4
3z + z2 = 0 + -4

Combine like terms: 0 + -4 = -4
3z + z2 = -4

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 = -4 + 2.25

Reorder the terms:
2.25 + 3z + z2 = -4 + 2.25

Combine like terms: -4 + 2.25 = -1.75
2.25 + 3z + z2 = -1.75

Factor a perfect square on the left side:
(z + 1.5)(z + 1.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.