x^2-65x+16=0

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

Simplifying
x2 + -65x + 16 = 0

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

Solving
16 + -65x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is -65x.  Take half its coefficient (-32.5).
Square it (1056.25) and add it to both sides.

Add '1056.25' to each side of the equation.
-65x + 1056.25 + x2 = -16 + 1056.25

Reorder the terms:
1056.25 + -65x + x2 = -16 + 1056.25

Combine like terms: -16 + 1056.25 = 1040.25
1056.25 + -65x + x2 = 1040.25

Factor a perfect square on the left side:
(x + -32.5)(x + -32.5) = 1040.25

Calculate the square root of the right side: 32.252906846

Break this problem into two subproblems by setting 
(x + -32.5) equal to 32.252906846 and -32.252906846.

Subproblem 1
x + -32.5 = 32.252906846

Simplifying
x + -32.5 = 32.252906846

Reorder the terms:
-32.5 + x = 32.252906846

Solving
-32.5 + x = 32.252906846

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '32.5' to each side of the equation.
-32.5 + 32.5 + x = 32.252906846 + 32.5

Combine like terms: -32.5 + 32.5 = 0.0
0.0 + x = 32.252906846 + 32.5
x = 32.252906846 + 32.5

Combine like terms: 32.252906846 + 32.5 = 64.752906846
x = 64.752906846

Simplifying
x = 64.752906846

Subproblem 2
x + -32.5 = -32.252906846

Simplifying
x + -32.5 = -32.252906846

Reorder the terms:
-32.5 + x = -32.252906846

Solving
-32.5 + x = -32.252906846

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '32.5' to each side of the equation.
-32.5 + 32.5 + x = -32.252906846 + 32.5

Combine like terms: -32.5 + 32.5 = 0.0
0.0 + x = -32.252906846 + 32.5
x = -32.252906846 + 32.5

Combine like terms: -32.252906846 + 32.5 = 0.247093154
x = 0.247093154

Simplifying
x = 0.247093154

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {64.752906846, 0.247093154}