a^2=22a+23

Solution for a^2=22a+23 equation:

Simplifying
a2 = 22a + 23

Reorder the terms:
a2 = 23 + 22a

Solving
a2 = 23 + 22a

Solving for variable 'a'.

Reorder the terms:
-23 + -22a + a2 = 23 + 22a + -23 + -22a

Reorder the terms:
-23 + -22a + a2 = 23 + -23 + 22a + -22a

Combine like terms: 23 + -23 = 0
-23 + -22a + a2 = 0 + 22a + -22a
-23 + -22a + a2 = 22a + -22a

Combine like terms: 22a + -22a = 0
-23 + -22a + a2 = 0

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

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

Simplifying
a = -1
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 = {-1, 23}