x^2-16x-65=0

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Solution for x^2-16x-65=0 equation: 


Simplifying
x2 + -16x + -65 = 0

Reorder the terms:
-65 + -16x + x2 = 0

Solving
-65 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '65' to each side of the equation.
-65 + -16x + 65 + x2 = 0 + 65

Reorder the terms:
-65 + 65 + -16x + x2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + -16x + x2 = 0 + 65
-16x + x2 = 0 + 65

Combine like terms: 0 + 65 = 65
-16x + x2 = 65

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 = 65 + 64

Reorder the terms:
64 + -16x + x2 = 65 + 64

Combine like terms: 65 + 64 = 129
64 + -16x + x2 = 129

Factor a perfect square on the left side:
(x + -8)(x + -8) = 129

Calculate the square root of the right side: 11.357816692

Break this problem into two subproblems by setting 
(x + -8) equal to 11.357816692 and -11.357816692.


Subproblem 1
x + -8 = 11.357816692

Simplifying
x + -8 = 11.357816692

Reorder the terms:
-8 + x = 11.357816692

Solving
-8 + x = 11.357816692

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 = 11.357816692 + 8

Combine like terms: -8 + 8 = 0
0 + x = 11.357816692 + 8
x = 11.357816692 + 8

Combine like terms: 11.357816692 + 8 = 19.357816692
x = 19.357816692

Simplifying
x = 19.357816692


Subproblem 2
x + -8 = -11.357816692

Simplifying
x + -8 = -11.357816692

Reorder the terms:
-8 + x = -11.357816692

Solving
-8 + x = -11.357816692

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 = -11.357816692 + 8

Combine like terms: -8 + 8 = 0
0 + x = -11.357816692 + 8
x = -11.357816692 + 8

Combine like terms: -11.357816692 + 8 = -3.357816692
x = -3.357816692

Simplifying
x = -3.357816692


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.357816692, -3.357816692}

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