x^2+16x+1=0

Solution for x^2+16x+1=0 equation:

Simplifying
x2 + 16x + 1 = 0

Reorder the terms:
1 + 16x + x2 = 0

Solving
1 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 16x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 16x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 16x + x2 = 0 + -1
16x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
16x + x2 = -1

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 = -1 + 64

Reorder the terms:
64 + 16x + x2 = -1 + 64

Combine like terms: -1 + 64 = 63
64 + 16x + x2 = 63

Factor a perfect square on the left side:
(x + 8)(x + 8) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + 8) equal to 7.937253933 and -7.937253933.

Subproblem 1
x + 8 = 7.937253933

Simplifying
x + 8 = 7.937253933

Reorder the terms:
8 + x = 7.937253933

Solving
8 + x = 7.937253933

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 = 7.937253933 + -8

Combine like terms: 8 + -8 = 0
0 + x = 7.937253933 + -8
x = 7.937253933 + -8

Combine like terms: 7.937253933 + -8 = -0.062746067
x = -0.062746067

Simplifying
x = -0.062746067

Subproblem 2
x + 8 = -7.937253933

Simplifying
x + 8 = -7.937253933

Reorder the terms:
8 + x = -7.937253933

Solving
8 + x = -7.937253933

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 = -7.937253933 + -8

Combine like terms: 8 + -8 = 0
0 + x = -7.937253933 + -8
x = -7.937253933 + -8

Combine like terms: -7.937253933 + -8 = -15.937253933
x = -15.937253933

Simplifying
x = -15.937253933

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.062746067, -15.937253933}