z^2+2z=33

Solution for z^2+2z=33 equation:

Simplifying
z2 + 2z = 33

Reorder the terms:
2z + z2 = 33

Solving
2z + z2 = 33

Solving for variable 'z'.

Reorder the terms:
-33 + 2z + z2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + 2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + 2z + 33 + z2 = 0 + 33

Reorder the terms:
-33 + 33 + 2z + z2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + 2z + z2 = 0 + 33
2z + z2 = 0 + 33

Combine like terms: 0 + 33 = 33
2z + z2 = 33

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 = 33 + 1

Reorder the terms:
1 + 2z + z2 = 33 + 1

Combine like terms: 33 + 1 = 34
1 + 2z + z2 = 34

Factor a perfect square on the left side:
(z + 1)(z + 1) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(z + 1) equal to 5.830951895 and -5.830951895.

Subproblem 1
z + 1 = 5.830951895

Simplifying
z + 1 = 5.830951895

Reorder the terms:
1 + z = 5.830951895

Solving
1 + z = 5.830951895

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 = 5.830951895 + -1

Combine like terms: 1 + -1 = 0
0 + z = 5.830951895 + -1
z = 5.830951895 + -1

Combine like terms: 5.830951895 + -1 = 4.830951895
z = 4.830951895

Simplifying
z = 4.830951895

Subproblem 2
z + 1 = -5.830951895

Simplifying
z + 1 = -5.830951895

Reorder the terms:
1 + z = -5.830951895

Solving
1 + z = -5.830951895

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 = -5.830951895 + -1

Combine like terms: 1 + -1 = 0
0 + z = -5.830951895 + -1
z = -5.830951895 + -1

Combine like terms: -5.830951895 + -1 = -6.830951895
z = -6.830951895

Simplifying
z = -6.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {4.830951895, -6.830951895}