a*a+9a-682=0

Solution for a*a+9a-682=0 equation:

Simplifying
a * a + 9a + -682 = 0

Multiply a * a
a2 + 9a + -682 = 0

Reorder the terms:
-682 + 9a + a2 = 0

Solving
-682 + 9a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-31 + -1a)(22 + -1a) = 0

Subproblem 1
Set the factor '(-31 + -1a)' equal to zero and attempt to solve:

Simplifying
-31 + -1a = 0

Solving
-31 + -1a = 0

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

Add '31' to each side of the equation.
-31 + 31 + -1a = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -1a = 0 + 31
-1a = 0 + 31

Combine like terms: 0 + 31 = 31
-1a = 31

Divide each side by '-1'.
a = -31

Simplifying
a = -31
Subproblem 2
Set the factor '(22 + -1a)' equal to zero and attempt to solve:

Simplifying
22 + -1a = 0

Solving
22 + -1a = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1a = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1a = 0 + -22
-1a = 0 + -22

Combine like terms: 0 + -22 = -22
-1a = -22

Divide each side by '-1'.
a = 22

Simplifying
a = 22
Solution
a = {-31, 22}