z^2+2z+13=0

Solution for z^2+2z+13=0 equation:

Simplifying
z2 + 2z + 13 = 0

Reorder the terms:
13 + 2z + z2 = 0

Solving
13 + 2z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 2z + -13 + z2 = 0 + -13

Reorder the terms:
13 + -13 + 2z + z2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 2z + z2 = 0 + -13
2z + z2 = 0 + -13

Combine like terms: 0 + -13 = -13
2z + z2 = -13

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 = -13 + 1

Reorder the terms:
1 + 2z + z2 = -13 + 1

Combine like terms: -13 + 1 = -12
1 + 2z + z2 = -12

Factor a perfect square on the left side:
(z + 1)(z + 1) = -12

Can't calculate square root of the right side.

The solution to this equation could not be determined.