z^2+7z+13=0

Solution for z^2+7z+13=0 equation:

Simplifying
z2 + 7z + 13 = 0

Reorder the terms:
13 + 7z + z2 = 0

Solving
13 + 7z + 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 + 7z + -13 + z2 = 0 + -13

Reorder the terms:
13 + -13 + 7z + z2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 7z + z2 = 0 + -13
7z + z2 = 0 + -13

Combine like terms: 0 + -13 = -13
7z + z2 = -13

The z term is 7z.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7z + 12.25 + z2 = -13 + 12.25

Reorder the terms:
12.25 + 7z + z2 = -13 + 12.25

Combine like terms: -13 + 12.25 = -0.75
12.25 + 7z + z2 = -0.75

Factor a perfect square on the left side:
(z + 3.5)(z + 3.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.