2z-z^2+11=0

Solution for 2z-z^2+11=0 equation:

Simplifying
2z + -1z2 + 11 = 0

Reorder the terms:
11 + 2z + -1z2 = 0

Solving
11 + 2z + -1z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-11 + -2z + z2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -2z + 11 + z2 = 0 + 11

Reorder the terms:
-11 + 11 + -2z + z2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2z + z2 = 0 + 11
-2z + z2 = 0 + 11

Combine like terms: 0 + 11 = 11
-2z + z2 = 11

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 = 11 + 1

Reorder the terms:
1 + -2z + z2 = 11 + 1

Combine like terms: 11 + 1 = 12
1 + -2z + z2 = 12

Factor a perfect square on the left side:
(z + -1)(z + -1) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(z + -1) equal to 3.464101615 and -3.464101615.

Subproblem 1
z + -1 = 3.464101615

Simplifying
z + -1 = 3.464101615

Reorder the terms:
-1 + z = 3.464101615

Solving
-1 + z = 3.464101615

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + z = 3.464101615 + 1

Combine like terms: -1 + 1 = 0
0 + z = 3.464101615 + 1
z = 3.464101615 + 1

Combine like terms: 3.464101615 + 1 = 4.464101615
z = 4.464101615

Simplifying
z = 4.464101615

Subproblem 2
z + -1 = -3.464101615

Simplifying
z + -1 = -3.464101615

Reorder the terms:
-1 + z = -3.464101615

Solving
-1 + z = -3.464101615

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + z = -3.464101615 + 1

Combine like terms: -1 + 1 = 0
0 + z = -3.464101615 + 1
z = -3.464101615 + 1

Combine like terms: -3.464101615 + 1 = -2.464101615
z = -2.464101615

Simplifying
z = -2.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {4.464101615, -2.464101615}