z^2+12z+45=0

Solution for z^2+12z+45=0 equation:

Simplifying
z2 + 12z + 45 = 0

Reorder the terms:
45 + 12z + z2 = 0

Solving
45 + 12z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + 12z + -45 + z2 = 0 + -45

Reorder the terms:
45 + -45 + 12z + z2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + 12z + z2 = 0 + -45
12z + z2 = 0 + -45

Combine like terms: 0 + -45 = -45
12z + z2 = -45

The z term is 12z.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12z + 36 + z2 = -45 + 36

Reorder the terms:
36 + 12z + z2 = -45 + 36

Combine like terms: -45 + 36 = -9
36 + 12z + z2 = -9

Factor a perfect square on the left side:
(z + 6)(z + 6) = -9

Can't calculate square root of the right side.

The solution to this equation could not be determined.