x^2+16x-208=0

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Solution for x^2+16x-208=0 equation: 


Simplifying
x2 + 16x + -208 = 0

Reorder the terms:
-208 + 16x + x2 = 0

Solving
-208 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '208' to each side of the equation.
-208 + 16x + 208 + x2 = 0 + 208

Reorder the terms:
-208 + 208 + 16x + x2 = 0 + 208

Combine like terms: -208 + 208 = 0
0 + 16x + x2 = 0 + 208
16x + x2 = 0 + 208

Combine like terms: 0 + 208 = 208
16x + x2 = 208

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 = 208 + 64

Reorder the terms:
64 + 16x + x2 = 208 + 64

Combine like terms: 208 + 64 = 272
64 + 16x + x2 = 272

Factor a perfect square on the left side:
(x + 8)(x + 8) = 272

Calculate the square root of the right side: 16.492422502

Break this problem into two subproblems by setting 
(x + 8) equal to 16.492422502 and -16.492422502.


Subproblem 1
x + 8 = 16.492422502

Simplifying
x + 8 = 16.492422502

Reorder the terms:
8 + x = 16.492422502

Solving
8 + x = 16.492422502

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 = 16.492422502 + -8

Combine like terms: 8 + -8 = 0
0 + x = 16.492422502 + -8
x = 16.492422502 + -8

Combine like terms: 16.492422502 + -8 = 8.492422502
x = 8.492422502

Simplifying
x = 8.492422502


Subproblem 2
x + 8 = -16.492422502

Simplifying
x + 8 = -16.492422502

Reorder the terms:
8 + x = -16.492422502

Solving
8 + x = -16.492422502

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 = -16.492422502 + -8

Combine like terms: 8 + -8 = 0
0 + x = -16.492422502 + -8
x = -16.492422502 + -8

Combine like terms: -16.492422502 + -8 = -24.492422502
x = -24.492422502

Simplifying
x = -24.492422502


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.492422502, -24.492422502}

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