x^2-36x+128=x

Solution for x^2-36x+128=x equation:

Simplifying
x2 + -36x + 128 = x

Reorder the terms:
128 + -36x + x2 = x

Solving
128 + -36x + x2 = x

Solving for variable 'x'.

Reorder the terms:
128 + -36x + -1x + x2 = x + -1x

Combine like terms: -36x + -1x = -37x
128 + -37x + x2 = x + -1x

Combine like terms: x + -1x = 0
128 + -37x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-128' to each side of the equation.
128 + -37x + -128 + x2 = 0 + -128

Reorder the terms:
128 + -128 + -37x + x2 = 0 + -128

Combine like terms: 128 + -128 = 0
0 + -37x + x2 = 0 + -128
-37x + x2 = 0 + -128

Combine like terms: 0 + -128 = -128
-37x + x2 = -128

The x term is -37x.  Take half its coefficient (-18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
-37x + 342.25 + x2 = -128 + 342.25

Reorder the terms:
342.25 + -37x + x2 = -128 + 342.25

Combine like terms: -128 + 342.25 = 214.25
342.25 + -37x + x2 = 214.25

Factor a perfect square on the left side:
(x + -18.5)(x + -18.5) = 214.25

Calculate the square root of the right side: 14.637281168

Break this problem into two subproblems by setting 
(x + -18.5) equal to 14.637281168 and -14.637281168.

Subproblem 1
x + -18.5 = 14.637281168

Simplifying
x + -18.5 = 14.637281168

Reorder the terms:
-18.5 + x = 14.637281168

Solving
-18.5 + x = 14.637281168

Solving for variable 'x'.

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

Add '18.5' to each side of the equation.
-18.5 + 18.5 + x = 14.637281168 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x = 14.637281168 + 18.5
x = 14.637281168 + 18.5

Combine like terms: 14.637281168 + 18.5 = 33.137281168
x = 33.137281168

Simplifying
x = 33.137281168

Subproblem 2
x + -18.5 = -14.637281168

Simplifying
x + -18.5 = -14.637281168

Reorder the terms:
-18.5 + x = -14.637281168

Solving
-18.5 + x = -14.637281168

Solving for variable 'x'.

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

Add '18.5' to each side of the equation.
-18.5 + 18.5 + x = -14.637281168 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x = -14.637281168 + 18.5
x = -14.637281168 + 18.5

Combine like terms: -14.637281168 + 18.5 = 3.862718832
x = 3.862718832

Simplifying
x = 3.862718832

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {33.137281168, 3.862718832}