x^2-16x-2=0

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


Simplifying
x2 + -16x + -2 = 0

Reorder the terms:
-2 + -16x + x2 = 0

Solving
-2 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -16x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -16x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -16x + x2 = 0 + 2
-16x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-16x + x2 = 2

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 = 2 + 64

Reorder the terms:
64 + -16x + x2 = 2 + 64

Combine like terms: 2 + 64 = 66
64 + -16x + x2 = 66

Factor a perfect square on the left side:
(x + -8)(x + -8) = 66

Calculate the square root of the right side: 8.124038405

Break this problem into two subproblems by setting 
(x + -8) equal to 8.124038405 and -8.124038405.


Subproblem 1
x + -8 = 8.124038405

Simplifying
x + -8 = 8.124038405

Reorder the terms:
-8 + x = 8.124038405

Solving
-8 + x = 8.124038405

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 = 8.124038405 + 8

Combine like terms: -8 + 8 = 0
0 + x = 8.124038405 + 8
x = 8.124038405 + 8

Combine like terms: 8.124038405 + 8 = 16.124038405
x = 16.124038405

Simplifying
x = 16.124038405


Subproblem 2
x + -8 = -8.124038405

Simplifying
x + -8 = -8.124038405

Reorder the terms:
-8 + x = -8.124038405

Solving
-8 + x = -8.124038405

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 = -8.124038405 + 8

Combine like terms: -8 + 8 = 0
0 + x = -8.124038405 + 8
x = -8.124038405 + 8

Combine like terms: -8.124038405 + 8 = -0.124038405
x = -0.124038405

Simplifying
x = -0.124038405


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.124038405, -0.124038405}

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