x(x+1)=483

Solution for x(x+1)=483 equation:

Simplifying
x(x + 1) = 483

Reorder the terms:
x(1 + x) = 483
(1 * x + x * x) = 483
(1x + x2) = 483

Solving
1x + x2 = 483

Solving for variable 'x'.

Reorder the terms:
-483 + 1x + x2 = 483 + -483

Combine like terms: 483 + -483 = 0
-483 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '483' to each side of the equation.
-483 + 1x + 483 + x2 = 0 + 483

Reorder the terms:
-483 + 483 + 1x + x2 = 0 + 483

Combine like terms: -483 + 483 = 0
0 + 1x + x2 = 0 + 483
1x + x2 = 0 + 483

Combine like terms: 0 + 483 = 483
1x + x2 = 483

The x term is 1x.  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.
x + 0.25 + x2 = 483 + 0.25

Reorder the terms:
0.25 + x + x2 = 483 + 0.25

Combine like terms: 483 + 0.25 = 483.25
0.25 + x + x2 = 483.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 483.25

Calculate the square root of the right side: 21.982947937

Break this problem into two subproblems by setting 
(x + 0.5) equal to 21.982947937 and -21.982947937.

Subproblem 1
x + 0.5 = 21.982947937

Simplifying
x + 0.5 = 21.982947937

Reorder the terms:
0.5 + x = 21.982947937

Solving
0.5 + x = 21.982947937

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 = 21.982947937 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 21.982947937 + -0.5
x = 21.982947937 + -0.5

Combine like terms: 21.982947937 + -0.5 = 21.482947937
x = 21.482947937

Simplifying
x = 21.482947937

Subproblem 2
x + 0.5 = -21.982947937

Simplifying
x + 0.5 = -21.982947937

Reorder the terms:
0.5 + x = -21.982947937

Solving
0.5 + x = -21.982947937

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 = -21.982947937 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -21.982947937 + -0.5
x = -21.982947937 + -0.5

Combine like terms: -21.982947937 + -0.5 = -22.482947937
x = -22.482947937

Simplifying
x = -22.482947937

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.482947937, -22.482947937}