z^2+14z+37=0

Solution for z^2+14z+37=0 equation:

Simplifying
z2 + 14z + 37 = 0

Reorder the terms:
37 + 14z + z2 = 0

Solving
37 + 14z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-37' to each side of the equation.
37 + 14z + -37 + z2 = 0 + -37

Reorder the terms:
37 + -37 + 14z + z2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 14z + z2 = 0 + -37
14z + z2 = 0 + -37

Combine like terms: 0 + -37 = -37
14z + z2 = -37

The z term is 14z.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14z + 49 + z2 = -37 + 49

Reorder the terms:
49 + 14z + z2 = -37 + 49

Combine like terms: -37 + 49 = 12
49 + 14z + z2 = 12

Factor a perfect square on the left side:
(z + 7)(z + 7) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(z + 7) equal to 3.464101615 and -3.464101615.

Subproblem 1
z + 7 = 3.464101615

Simplifying
z + 7 = 3.464101615

Reorder the terms:
7 + z = 3.464101615

Solving
7 + z = 3.464101615

Solving for variable 'z'.

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

Add '-7' to each side of the equation.
7 + -7 + z = 3.464101615 + -7

Combine like terms: 7 + -7 = 0
0 + z = 3.464101615 + -7
z = 3.464101615 + -7

Combine like terms: 3.464101615 + -7 = -3.535898385
z = -3.535898385

Simplifying
z = -3.535898385

Subproblem 2
z + 7 = -3.464101615

Simplifying
z + 7 = -3.464101615

Reorder the terms:
7 + z = -3.464101615

Solving
7 + z = -3.464101615

Solving for variable 'z'.

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

Add '-7' to each side of the equation.
7 + -7 + z = -3.464101615 + -7

Combine like terms: 7 + -7 = 0
0 + z = -3.464101615 + -7
z = -3.464101615 + -7

Combine like terms: -3.464101615 + -7 = -10.464101615
z = -10.464101615

Simplifying
z = -10.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-3.535898385, -10.464101615}