x^2-16x-3=0

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Solution for x^2-16x-3=0 equation: 


Simplifying
x2 + -16x + -3 = 0

Reorder the terms:
-3 + -16x + x2 = 0

Solving
-3 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -16x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -16x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -16x + x2 = 0 + 3
-16x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-16x + x2 = 3

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 = 3 + 64

Reorder the terms:
64 + -16x + x2 = 3 + 64

Combine like terms: 3 + 64 = 67
64 + -16x + x2 = 67

Factor a perfect square on the left side:
(x + -8)(x + -8) = 67

Calculate the square root of the right side: 8.185352772

Break this problem into two subproblems by setting 
(x + -8) equal to 8.185352772 and -8.185352772.


Subproblem 1
x + -8 = 8.185352772

Simplifying
x + -8 = 8.185352772

Reorder the terms:
-8 + x = 8.185352772

Solving
-8 + x = 8.185352772

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 = 8.185352772 + 8

Combine like terms: -8 + 8 = 0
0 + x = 8.185352772 + 8
x = 8.185352772 + 8

Combine like terms: 8.185352772 + 8 = 16.185352772
x = 16.185352772

Simplifying
x = 16.185352772


Subproblem 2
x + -8 = -8.185352772

Simplifying
x + -8 = -8.185352772

Reorder the terms:
-8 + x = -8.185352772

Solving
-8 + x = -8.185352772

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 = -8.185352772 + 8

Combine like terms: -8 + 8 = 0
0 + x = -8.185352772 + 8
x = -8.185352772 + 8

Combine like terms: -8.185352772 + 8 = -0.185352772
x = -0.185352772

Simplifying
x = -0.185352772


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.185352772, -0.185352772}

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