x^2-16x-1=0

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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 = 65
64 + -16x + x2 = 65

Factor a perfect square on the left side:
(x + -8)(x + -8) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x + -8) equal to 8.062257748 and -8.062257748.


Subproblem 1
x + -8 = 8.062257748

Simplifying
x + -8 = 8.062257748

Reorder the terms:
-8 + x = 8.062257748

Solving
-8 + x = 8.062257748

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 = 8.062257748 + 8

Combine like terms: -8 + 8 = 0
0 + x = 8.062257748 + 8
x = 8.062257748 + 8

Combine like terms: 8.062257748 + 8 = 16.062257748
x = 16.062257748

Simplifying
x = 16.062257748


Subproblem 2
x + -8 = -8.062257748

Simplifying
x + -8 = -8.062257748

Reorder the terms:
-8 + x = -8.062257748

Solving
-8 + x = -8.062257748

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 = -8.062257748 + 8

Combine like terms: -8 + 8 = 0
0 + x = -8.062257748 + 8
x = -8.062257748 + 8

Combine like terms: -8.062257748 + 8 = -0.062257748
x = -0.062257748

Simplifying
x = -0.062257748


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.062257748, -0.062257748}

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