z^2+6z+2=

Solution for z^2+6z+2= equation:

Simplifying
z2 + 6z + 2 = 0

Reorder the terms:
2 + 6z + z2 = 0

Solving
2 + 6z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 6z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + 6z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 6z + z2 = 0 + -2
6z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
6z + z2 = -2

The z term is 6z.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6z + 9 + z2 = -2 + 9

Reorder the terms:
9 + 6z + z2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + 6z + z2 = 7

Factor a perfect square on the left side:
(z + 3)(z + 3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(z + 3) equal to 2.645751311 and -2.645751311.

Subproblem 1
z + 3 = 2.645751311

Simplifying
z + 3 = 2.645751311

Reorder the terms:
3 + z = 2.645751311

Solving
3 + z = 2.645751311

Solving for variable 'z'.

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

Add '-3' to each side of the equation.
3 + -3 + z = 2.645751311 + -3

Combine like terms: 3 + -3 = 0
0 + z = 2.645751311 + -3
z = 2.645751311 + -3

Combine like terms: 2.645751311 + -3 = -0.354248689
z = -0.354248689

Simplifying
z = -0.354248689

Subproblem 2
z + 3 = -2.645751311

Simplifying
z + 3 = -2.645751311

Reorder the terms:
3 + z = -2.645751311

Solving
3 + z = -2.645751311

Solving for variable 'z'.

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

Add '-3' to each side of the equation.
3 + -3 + z = -2.645751311 + -3

Combine like terms: 3 + -3 = 0
0 + z = -2.645751311 + -3
z = -2.645751311 + -3

Combine like terms: -2.645751311 + -3 = -5.645751311
z = -5.645751311

Simplifying
z = -5.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-0.354248689, -5.645751311}