a^2-8a=209

Solution for a^2-8a=209 equation:

Simplifying
a2 + -8a = 209

Reorder the terms:
-8a + a2 = 209

Solving
-8a + a2 = 209

Solving for variable 'a'.

Reorder the terms:
-209 + -8a + a2 = 209 + -209

Combine like terms: 209 + -209 = 0
-209 + -8a + a2 = 0

Factor a trinomial.
(-11 + -1a)(19 + -1a) = 0

Subproblem 1
Set the factor '(-11 + -1a)' equal to zero and attempt to solve:

Simplifying
-11 + -1a = 0

Solving
-11 + -1a = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1a = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1a = 0 + 11
-1a = 0 + 11

Combine like terms: 0 + 11 = 11
-1a = 11

Divide each side by '-1'.
a = -11

Simplifying
a = -11
Subproblem 2
Set the factor '(19 + -1a)' equal to zero and attempt to solve:

Simplifying
19 + -1a = 0

Solving
19 + -1a = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1a = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1a = 0 + -19
-1a = 0 + -19

Combine like terms: 0 + -19 = -19
-1a = -19

Divide each side by '-1'.
a = 19

Simplifying
a = 19
Solution
a = {-11, 19}