z^2+2z-50=0

Solution for z^2+2z-50=0 equation:

Simplifying
z2 + 2z + -50 = 0

Reorder the terms:
-50 + 2z + z2 = 0

Solving
-50 + 2z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 2z + 50 + z2 = 0 + 50

Reorder the terms:
-50 + 50 + 2z + z2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 2z + z2 = 0 + 50
2z + z2 = 0 + 50

Combine like terms: 0 + 50 = 50
2z + z2 = 50

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 = 50 + 1

Reorder the terms:
1 + 2z + z2 = 50 + 1

Combine like terms: 50 + 1 = 51
1 + 2z + z2 = 51

Factor a perfect square on the left side:
(z + 1)(z + 1) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(z + 1) equal to 7.141428429 and -7.141428429.

Subproblem 1
z + 1 = 7.141428429

Simplifying
z + 1 = 7.141428429

Reorder the terms:
1 + z = 7.141428429

Solving
1 + z = 7.141428429

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 = 7.141428429 + -1

Combine like terms: 1 + -1 = 0
0 + z = 7.141428429 + -1
z = 7.141428429 + -1

Combine like terms: 7.141428429 + -1 = 6.141428429
z = 6.141428429

Simplifying
z = 6.141428429

Subproblem 2
z + 1 = -7.141428429

Simplifying
z + 1 = -7.141428429

Reorder the terms:
1 + z = -7.141428429

Solving
1 + z = -7.141428429

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 = -7.141428429 + -1

Combine like terms: 1 + -1 = 0
0 + z = -7.141428429 + -1
z = -7.141428429 + -1

Combine like terms: -7.141428429 + -1 = -8.141428429
z = -8.141428429

Simplifying
z = -8.141428429

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {6.141428429, -8.141428429}