289+34a+a^2=2209

Solution for 289+34a+a^2=2209 equation:

Simplifying
289 + 34a + a2 = 2209

Solving
289 + 34a + a2 = 2209

Solving for variable 'a'.

Reorder the terms:
289 + -2209 + 34a + a2 = 2209 + -2209

Combine like terms: 289 + -2209 = -1920
-1920 + 34a + a2 = 2209 + -2209

Combine like terms: 2209 + -2209 = 0
-1920 + 34a + a2 = 0

Factor a trinomial.
(-64 + -1a)(30 + -1a) = 0

Subproblem 1
Set the factor '(-64 + -1a)' equal to zero and attempt to solve:

Simplifying
-64 + -1a = 0

Solving
-64 + -1a = 0

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

Add '64' to each side of the equation.
-64 + 64 + -1a = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -1a = 0 + 64
-1a = 0 + 64

Combine like terms: 0 + 64 = 64
-1a = 64

Divide each side by '-1'.
a = -64

Simplifying
a = -64
Subproblem 2
Set the factor '(30 + -1a)' equal to zero and attempt to solve:

Simplifying
30 + -1a = 0

Solving
30 + -1a = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1a = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1a = 0 + -30
-1a = 0 + -30

Combine like terms: 0 + -30 = -30
-1a = -30

Divide each side by '-1'.
a = 30

Simplifying
a = 30
Solution
a = {-64, 30}