x^2+16x+32=0

Solution for x^2+16x+32=0 equation:

Simplifying
x2 + 16x + 32 = 0

Reorder the terms:
32 + 16x + x2 = 0

Solving
32 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + 16x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + 16x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 16x + x2 = 0 + -32
16x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
16x + x2 = -32

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -32 + 64

Reorder the terms:
64 + 16x + x2 = -32 + 64

Combine like terms: -32 + 64 = 32
64 + 16x + x2 = 32

Factor a perfect square on the left side:
(x + 8)(x + 8) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + 8) equal to 5.656854249 and -5.656854249.

Subproblem 1
x + 8 = 5.656854249

Simplifying
x + 8 = 5.656854249

Reorder the terms:
8 + x = 5.656854249

Solving
8 + x = 5.656854249

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 5.656854249 + -8

Combine like terms: 8 + -8 = 0
0 + x = 5.656854249 + -8
x = 5.656854249 + -8

Combine like terms: 5.656854249 + -8 = -2.343145751
x = -2.343145751

Simplifying
x = -2.343145751

Subproblem 2
x + 8 = -5.656854249

Simplifying
x + 8 = -5.656854249

Reorder the terms:
8 + x = -5.656854249

Solving
8 + x = -5.656854249

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -5.656854249 + -8

Combine like terms: 8 + -8 = 0
0 + x = -5.656854249 + -8
x = -5.656854249 + -8

Combine like terms: -5.656854249 + -8 = -13.656854249
x = -13.656854249

Simplifying
x = -13.656854249

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.343145751, -13.656854249}