600.6+x=x^2

Solution for 600.6+x=x^2 equation:

Simplifying
600.6 + x = x2

Solving
600.6 + x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
600.6 + x + -1x2 = 0

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

Divide each side by '-1'.
-600.6 + -1x + x2 = 0

Move the constant term to the right:

Add '600.6' to each side of the equation.
-600.6 + -1x + 600.6 + x2 = 0 + 600.6

Reorder the terms:
-600.6 + 600.6 + -1x + x2 = 0 + 600.6

Combine like terms: -600.6 + 600.6 = 0.0
0.0 + -1x + x2 = 0 + 600.6
-1x + x2 = 0 + 600.6

Combine like terms: 0 + 600.6 = 600.6
-1x + x2 = 600.6

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 600.6 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 600.6 + 0.25

Combine like terms: 600.6 + 0.25 = 600.85
0.25 + -1x + x2 = 600.85

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 600.85

Calculate the square root of the right side: 24.51224184

Break this problem into two subproblems by setting 
(x + 0.5) equal to 24.51224184 and -24.51224184.

Subproblem 1
x + 0.5 = 24.51224184

Simplifying
x + 0.5 = 24.51224184

Reorder the terms:
0.5 + x = 24.51224184

Solving
0.5 + x = 24.51224184

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 24.51224184 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 24.51224184 + -0.5
x = 24.51224184 + -0.5

Combine like terms: 24.51224184 + -0.5 = 24.01224184
x = 24.01224184

Simplifying
x = 24.01224184

Subproblem 2
x + 0.5 = -24.51224184

Simplifying
x + 0.5 = -24.51224184

Reorder the terms:
0.5 + x = -24.51224184

Solving
0.5 + x = -24.51224184

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -24.51224184 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -24.51224184 + -0.5
x = -24.51224184 + -0.5

Combine like terms: -24.51224184 + -0.5 = -25.01224184
x = -25.01224184

Simplifying
x = -25.01224184

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.01224184, -25.01224184}