Answer: a = ±√11
Step-by-step explanation: To solve for a, we can begin by rewriting the problem in numeric form:
[tex]-31 \ = \ 2 \ - \ 3a^{2}[/tex]
Next, we can subtract 2 from both sides:
⇒ [tex]-33 \ = \ -3a^{2}[/tex]
Then, we divide by the coefficient (-3):
⇒ [tex]11 \ = \ a^{2}[/tex]
To solve for a, we find the square root of both sides. Therefore, the simplest radical form of the equation would be a = ±√11.