x(x+1)=552

Solution for x(x+1)=552 equation:

Simplifying
x(x + 1) = 552

Reorder the terms:
x(1 + x) = 552
(1 * x + x * x) = 552
(1x + x2) = 552

Solving
1x + x2 = 552

Solving for variable 'x'.

Reorder the terms:
-552 + 1x + x2 = 552 + -552

Combine like terms: 552 + -552 = 0
-552 + 1x + x2 = 0

Factor a trinomial.
(-24 + -1x)(23 + -1x) = 0

Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x = 0 + 24
-1x = 0 + 24

Combine like terms: 0 + 24 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24
Subproblem 2
Set the factor '(23 + -1x)' equal to zero and attempt to solve:

Simplifying
23 + -1x = 0

Solving
23 + -1x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -1x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -1x = 0 + -23
-1x = 0 + -23

Combine like terms: 0 + -23 = -23
-1x = -23

Divide each side by '-1'.
x = 23

Simplifying
x = 23
Solution
x = {-24, 23}