Z^2+4Z+5=0

Solution for Z^2+4Z+5=0 equation:

Simplifying
Z2 + 4Z + 5 = 0

Reorder the terms:
5 + 4Z + Z2 = 0

Solving
5 + 4Z + Z2 = 0

Solving for variable 'Z'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 4Z + -5 + Z2 = 0 + -5

Reorder the terms:
5 + -5 + 4Z + Z2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4Z + Z2 = 0 + -5
4Z + Z2 = 0 + -5

Combine like terms: 0 + -5 = -5
4Z + Z2 = -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 = -5 + 4

Reorder the terms:
4 + 4Z + Z2 = -5 + 4

Combine like terms: -5 + 4 = -1
4 + 4Z + Z2 = -1

Factor a perfect square on the left side:
(Z + 2)(Z + 2) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.