x^2-16x-272=0

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Solution for x^2-16x-272=0 equation: 


Simplifying
x2 + -16x + -272 = 0

Reorder the terms:
-272 + -16x + x2 = 0

Solving
-272 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '272' to each side of the equation.
-272 + -16x + 272 + x2 = 0 + 272

Reorder the terms:
-272 + 272 + -16x + x2 = 0 + 272

Combine like terms: -272 + 272 = 0
0 + -16x + x2 = 0 + 272
-16x + x2 = 0 + 272

Combine like terms: 0 + 272 = 272
-16x + x2 = 272

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 = 272 + 64

Reorder the terms:
64 + -16x + x2 = 272 + 64

Combine like terms: 272 + 64 = 336
64 + -16x + x2 = 336

Factor a perfect square on the left side:
(x + -8)(x + -8) = 336

Calculate the square root of the right side: 18.33030278

Break this problem into two subproblems by setting 
(x + -8) equal to 18.33030278 and -18.33030278.


Subproblem 1
x + -8 = 18.33030278

Simplifying
x + -8 = 18.33030278

Reorder the terms:
-8 + x = 18.33030278

Solving
-8 + x = 18.33030278

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 = 18.33030278 + 8

Combine like terms: -8 + 8 = 0
0 + x = 18.33030278 + 8
x = 18.33030278 + 8

Combine like terms: 18.33030278 + 8 = 26.33030278
x = 26.33030278

Simplifying
x = 26.33030278


Subproblem 2
x + -8 = -18.33030278

Simplifying
x + -8 = -18.33030278

Reorder the terms:
-8 + x = -18.33030278

Solving
-8 + x = -18.33030278

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 = -18.33030278 + 8

Combine like terms: -8 + 8 = 0
0 + x = -18.33030278 + 8
x = -18.33030278 + 8

Combine like terms: -18.33030278 + 8 = -10.33030278
x = -10.33030278

Simplifying
x = -10.33030278


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.33030278, -10.33030278}

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