x^2-60x-900=x

Solution for x^2-60x-900=x equation:

Simplifying
x2 + -60x + -900 = x

Reorder the terms:
-900 + -60x + x2 = x

Solving
-900 + -60x + x2 = x

Solving for variable 'x'.

Reorder the terms:
-900 + -60x + -1x + x2 = x + -1x

Combine like terms: -60x + -1x = -61x
-900 + -61x + x2 = x + -1x

Combine like terms: x + -1x = 0
-900 + -61x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '900' to each side of the equation.
-900 + -61x + 900 + x2 = 0 + 900

Reorder the terms:
-900 + 900 + -61x + x2 = 0 + 900

Combine like terms: -900 + 900 = 0
0 + -61x + x2 = 0 + 900
-61x + x2 = 0 + 900

Combine like terms: 0 + 900 = 900
-61x + x2 = 900

The x term is -61x.  Take half its coefficient (-30.5).
Square it (930.25) and add it to both sides.

Add '930.25' to each side of the equation.
-61x + 930.25 + x2 = 900 + 930.25

Reorder the terms:
930.25 + -61x + x2 = 900 + 930.25

Combine like terms: 900 + 930.25 = 1830.25
930.25 + -61x + x2 = 1830.25

Factor a perfect square on the left side:
(x + -30.5)(x + -30.5) = 1830.25

Calculate the square root of the right side: 42.781421201

Break this problem into two subproblems by setting 
(x + -30.5) equal to 42.781421201 and -42.781421201.

Subproblem 1
x + -30.5 = 42.781421201

Simplifying
x + -30.5 = 42.781421201

Reorder the terms:
-30.5 + x = 42.781421201

Solving
-30.5 + x = 42.781421201

Solving for variable 'x'.

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

Add '30.5' to each side of the equation.
-30.5 + 30.5 + x = 42.781421201 + 30.5

Combine like terms: -30.5 + 30.5 = 0.0
0.0 + x = 42.781421201 + 30.5
x = 42.781421201 + 30.5

Combine like terms: 42.781421201 + 30.5 = 73.281421201
x = 73.281421201

Simplifying
x = 73.281421201

Subproblem 2
x + -30.5 = -42.781421201

Simplifying
x + -30.5 = -42.781421201

Reorder the terms:
-30.5 + x = -42.781421201

Solving
-30.5 + x = -42.781421201

Solving for variable 'x'.

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

Add '30.5' to each side of the equation.
-30.5 + 30.5 + x = -42.781421201 + 30.5

Combine like terms: -30.5 + 30.5 = 0.0
0.0 + x = -42.781421201 + 30.5
x = -42.781421201 + 30.5

Combine like terms: -42.781421201 + 30.5 = -12.281421201
x = -12.281421201

Simplifying
x = -12.281421201

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {73.281421201, -12.281421201}