z^2=-2z-20

Solution for z^2=-2z-20 equation:

Simplifying
z2 = -2z + -20

Reorder the terms:
z2 = -20 + -2z

Solving
z2 = -20 + -2z

Solving for variable 'z'.

Reorder the terms:
20 + 2z + z2 = -20 + -2z + 20 + 2z

Reorder the terms:
20 + 2z + z2 = -20 + 20 + -2z + 2z

Combine like terms: -20 + 20 = 0
20 + 2z + z2 = 0 + -2z + 2z
20 + 2z + z2 = -2z + 2z

Combine like terms: -2z + 2z = 0
20 + 2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 2z + -20 + z2 = 0 + -20

Reorder the terms:
20 + -20 + 2z + z2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 2z + z2 = 0 + -20
2z + z2 = 0 + -20

Combine like terms: 0 + -20 = -20
2z + z2 = -20

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 = -20 + 1

Reorder the terms:
1 + 2z + z2 = -20 + 1

Combine like terms: -20 + 1 = -19
1 + 2z + z2 = -19

Factor a perfect square on the left side:
(z + 1)(z + 1) = -19

Can't calculate square root of the right side.

The solution to this equation could not be determined.