z^2+z+4=0

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

Simplifying
z2 + z + 4 = 0

Reorder the terms:
4 + z + z2 = 0

Solving
4 + z + 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 + z + -4 + z2 = 0 + -4

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

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

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

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
z + 0.25 + z2 = -4 + 0.25

Reorder the terms:
0.25 + z + z2 = -4 + 0.25

Combine like terms: -4 + 0.25 = -3.75
0.25 + z + z2 = -3.75

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.