=z^2+2z+2

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

Simplifying
0 = z2 + 2z + 2

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

Solving
0 = 2 + 2z + z2

Solving for variable 'z'.

Combine like terms: 0 + -2 = -2
-2 + -2z + -1z2 = 2 + 2z + z2 + -2 + -2z + -1z2

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

Combine like terms: 2 + -2 = 0
-2 + -2z + -1z2 = 0 + 2z + -2z + z2 + -1z2
-2 + -2z + -1z2 = 2z + -2z + z2 + -1z2

Combine like terms: 2z + -2z = 0
-2 + -2z + -1z2 = 0 + z2 + -1z2
-2 + -2z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-2 + -2z + -1z2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 2z + z2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 2z + z2)' equal to zero and attempt to solve:

Simplifying
2 + 2z + z2 = 0

Solving
2 + 2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -2 + 1

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

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

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

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.