Answer
{$-3,3$}
Work Step by Step
Since $7$ is common to both the terms of the equation, we take it out as a common factor:
$7x^{2}=63$
$7x^{2}-63=0$
$7(x^{2}-9)=0$
$(x^{2}-9)=0$
We simplify the expression further using the rule $a^{2}-b^{2}=(a+b)(a-b)$:
$(x^{2}-9)=0$
$(x^{2}-3^{2})=0$
$(x+3)(x-3)=0$
Now, we equate all of the factors to zero to solve the equation:
$(x+3)(x-3)=0$
$x+3=0$ or $(x-3)=0$
$x=-3$ or $x=3$
Therefore, the solution set is {$-3,3$}.
