2z^2+2z+13=0

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

Simplifying
2z2 + 2z + 13 = 0

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

Solving
13 + 2z + 2z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
6.5 + z + z2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + z + -6.5 + z2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + z + z2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + z + z2 = 0 + -6.5
z + z2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
z + z2 = -6.5

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.
 + 0.25 + z2 = -6.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + z2 = -6.5 + 0.25

Combine like terms: -6.5 + 0.25 = -6.25
1.25 + z2 = -6.25

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -6.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.