We can check our answers by substituting them for a in the given equation. Let's start with a=- sqrt(111).
a^2+6^2=( 7sqrt(3))^2
( - sqrt(111))^2+6^2? =( 7sqrt(3))^2
( sqrt(111))^2+6^2? =( 7sqrt(3))^2
111+6^2? =( 7sqrt(3))^2
111+36? =49* 3
111+36? =147
147=147 ✓
Since 147=147, we know that a=- sqrt(111) is a solution of the equation. Let's check if a=sqrt(111) is also a solution.
a^2+6^2=(7sqrt(3))^2
( sqrt(111))^2+6^2? =(7sqrt(3))^2
111+6^2? =(7sqrt(3))^2
111+36? =49* 3
111+36? =147
147=147 ✓
Again, since 147=147, we know that a=sqrt(111) is a solution of the equation.
