0=x^2+16x-6

Solution for 0=x^2+16x-6 equation:

Simplifying
0 = x2 + 16x + -6

Reorder the terms:
0 = -6 + 16x + x2

Solving
0 = -6 + 16x + x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + -16x + -1x2 = -6 + 16x + x2 + 6 + -16x + -1x2

Reorder the terms:
6 + -16x + -1x2 = -6 + 6 + 16x + -16x + x2 + -1x2

Combine like terms: -6 + 6 = 0
6 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2
6 + -16x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
6 + -16x + -1x2 = 0 + x2 + -1x2
6 + -16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -16x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 16x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 16x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 16x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 16x + x2 = 0 + 6
16x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
16x + x2 = 6

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 = 6 + 64

Reorder the terms:
64 + 16x + x2 = 6 + 64

Combine like terms: 6 + 64 = 70
64 + 16x + x2 = 70

Factor a perfect square on the left side:
(x + 8)(x + 8) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(x + 8) equal to 8.366600265 and -8.366600265.

Subproblem 1
x + 8 = 8.366600265

Simplifying
x + 8 = 8.366600265

Reorder the terms:
8 + x = 8.366600265

Solving
8 + x = 8.366600265

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 = 8.366600265 + -8

Combine like terms: 8 + -8 = 0
0 + x = 8.366600265 + -8
x = 8.366600265 + -8

Combine like terms: 8.366600265 + -8 = 0.366600265
x = 0.366600265

Simplifying
x = 0.366600265

Subproblem 2
x + 8 = -8.366600265

Simplifying
x + 8 = -8.366600265

Reorder the terms:
8 + x = -8.366600265

Solving
8 + x = -8.366600265

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 = -8.366600265 + -8

Combine like terms: 8 + -8 = 0
0 + x = -8.366600265 + -8
x = -8.366600265 + -8

Combine like terms: -8.366600265 + -8 = -16.366600265
x = -16.366600265

Simplifying
x = -16.366600265

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.366600265, -16.366600265}