0=x^2-16x+34

Solution for 0=x^2-16x+34 equation:

Simplifying
0 = x2 + -16x + 34

Reorder the terms:
0 = 34 + -16x + x2

Solving
0 = 34 + -16x + x2

Solving for variable 'x'.

Combine like terms: 0 + -34 = -34
-34 + 16x + -1x2 = 34 + -16x + x2 + -34 + 16x + -1x2

Reorder the terms:
-34 + 16x + -1x2 = 34 + -34 + -16x + 16x + x2 + -1x2

Combine like terms: 34 + -34 = 0
-34 + 16x + -1x2 = 0 + -16x + 16x + x2 + -1x2
-34 + 16x + -1x2 = -16x + 16x + x2 + -1x2

Combine like terms: -16x + 16x = 0
-34 + 16x + -1x2 = 0 + x2 + -1x2
-34 + 16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-34 + 16x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
34 + -16x + x2 = 0

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + -16x + -34 + x2 = 0 + -34

Reorder the terms:
34 + -34 + -16x + x2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -16x + x2 = 0 + -34
-16x + x2 = 0 + -34

Combine like terms: 0 + -34 = -34
-16x + x2 = -34

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 = -34 + 64

Reorder the terms:
64 + -16x + x2 = -34 + 64

Combine like terms: -34 + 64 = 30
64 + -16x + x2 = 30

Factor a perfect square on the left side:
(x + -8)(x + -8) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + -8) equal to 5.477225575 and -5.477225575.

Subproblem 1
x + -8 = 5.477225575

Simplifying
x + -8 = 5.477225575

Reorder the terms:
-8 + x = 5.477225575

Solving
-8 + x = 5.477225575

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 = 5.477225575 + 8

Combine like terms: -8 + 8 = 0
0 + x = 5.477225575 + 8
x = 5.477225575 + 8

Combine like terms: 5.477225575 + 8 = 13.477225575
x = 13.477225575

Simplifying
x = 13.477225575

Subproblem 2
x + -8 = -5.477225575

Simplifying
x + -8 = -5.477225575

Reorder the terms:
-8 + x = -5.477225575

Solving
-8 + x = -5.477225575

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 = -5.477225575 + 8

Combine like terms: -8 + 8 = 0
0 + x = -5.477225575 + 8
x = -5.477225575 + 8

Combine like terms: -5.477225575 + 8 = 2.522774425
x = 2.522774425

Simplifying
x = 2.522774425

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.477225575, 2.522774425}