x^2-18x+34=0

Solution for x^2-18x+34=0 equation:

Simplifying
x2 + -18x + 34 = 0

Reorder the terms:
34 + -18x + x2 = 0

Solving
34 + -18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + -18x + -34 + x2 = 0 + -34

Reorder the terms:
34 + -34 + -18x + x2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -18x + x2 = 0 + -34
-18x + x2 = 0 + -34

Combine like terms: 0 + -34 = -34
-18x + x2 = -34

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -34 + 81

Reorder the terms:
81 + -18x + x2 = -34 + 81

Combine like terms: -34 + 81 = 47
81 + -18x + x2 = 47

Factor a perfect square on the left side:
(x + -9)(x + -9) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(x + -9) equal to 6.8556546 and -6.8556546.

Subproblem 1
x + -9 = 6.8556546

Simplifying
x + -9 = 6.8556546

Reorder the terms:
-9 + x = 6.8556546

Solving
-9 + x = 6.8556546

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 6.8556546 + 9

Combine like terms: -9 + 9 = 0
0 + x = 6.8556546 + 9
x = 6.8556546 + 9

Combine like terms: 6.8556546 + 9 = 15.8556546
x = 15.8556546

Simplifying
x = 15.8556546

Subproblem 2
x + -9 = -6.8556546

Simplifying
x + -9 = -6.8556546

Reorder the terms:
-9 + x = -6.8556546

Solving
-9 + x = -6.8556546

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -6.8556546 + 9

Combine like terms: -9 + 9 = 0
0 + x = -6.8556546 + 9
x = -6.8556546 + 9

Combine like terms: -6.8556546 + 9 = 2.1443454
x = 2.1443454

Simplifying
x = 2.1443454

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.8556546, 2.1443454}