z^2+z+3=0

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

Simplifying
z2 + z + 3 = 0

Reorder the terms:
3 + z + z2 = 0

Solving
3 + z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -3 + 0.25

Reorder the terms:
0.25 + z + z2 = -3 + 0.25

Combine like terms: -3 + 0.25 = -2.75
0.25 + z + z2 = -2.75

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.