0=x^2+16x-128

Solution for 0=x^2+16x-128 equation:

Simplifying
0 = x2 + 16x + -128

Reorder the terms:
0 = -128 + 16x + x2

Solving
0 = -128 + 16x + x2

Solving for variable 'x'.

Combine like terms: 0 + 128 = 128
128 + -16x + -1x2 = -128 + 16x + x2 + 128 + -16x + -1x2

Reorder the terms:
128 + -16x + -1x2 = -128 + 128 + 16x + -16x + x2 + -1x2

Combine like terms: -128 + 128 = 0
128 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2
128 + -16x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
128 + -16x + -1x2 = 0 + x2 + -1x2
128 + -16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
128 + -16x + -1x2 = 0

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

Divide each side by '-1'.
-128 + 16x + x2 = 0

Move the constant term to the right:

Add '128' to each side of the equation.
-128 + 16x + 128 + x2 = 0 + 128

Reorder the terms:
-128 + 128 + 16x + x2 = 0 + 128

Combine like terms: -128 + 128 = 0
0 + 16x + x2 = 0 + 128
16x + x2 = 0 + 128

Combine like terms: 0 + 128 = 128
16x + x2 = 128

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 = 128 + 64

Reorder the terms:
64 + 16x + x2 = 128 + 64

Combine like terms: 128 + 64 = 192
64 + 16x + x2 = 192

Factor a perfect square on the left side:
(x + 8)(x + 8) = 192

Calculate the square root of the right side: 13.856406461

Break this problem into two subproblems by setting 
(x + 8) equal to 13.856406461 and -13.856406461.

Subproblem 1
x + 8 = 13.856406461

Simplifying
x + 8 = 13.856406461

Reorder the terms:
8 + x = 13.856406461

Solving
8 + x = 13.856406461

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 = 13.856406461 + -8

Combine like terms: 8 + -8 = 0
0 + x = 13.856406461 + -8
x = 13.856406461 + -8

Combine like terms: 13.856406461 + -8 = 5.856406461
x = 5.856406461

Simplifying
x = 5.856406461

Subproblem 2
x + 8 = -13.856406461

Simplifying
x + 8 = -13.856406461

Reorder the terms:
8 + x = -13.856406461

Solving
8 + x = -13.856406461

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 = -13.856406461 + -8

Combine like terms: 8 + -8 = 0
0 + x = -13.856406461 + -8
x = -13.856406461 + -8

Combine like terms: -13.856406461 + -8 = -21.856406461
x = -21.856406461

Simplifying
x = -21.856406461

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.856406461, -21.856406461}