a(a+1)=552

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

Simplifying
a(a + 1) = 552

Reorder the terms:
a(1 + a) = 552
(1 * a + a * a) = 552
(1a + a2) = 552

Solving
1a + a2 = 552

Solving for variable 'a'.

Reorder the terms:
-552 + 1a + a2 = 552 + -552

Combine like terms: 552 + -552 = 0
-552 + 1a + a2 = 0

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

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

Simplifying
-24 + -1a = 0

Solving
-24 + -1a = 0

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

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

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

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

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

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

Simplifying
23 + -1a = 0

Solving
23 + -1a = 0

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

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

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

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

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

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